item-item collab filtering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from surprise import KNNWithMeans\n",
    "from surprise import Dataset\n",
    "from surprise import accuracy\n",
    "from surprise.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the movielens-100k dataset  UserID::MovieID::Rating::Timestamp\n",
    "data = Dataset.load_builtin('ml-100k')\n",
    "trainset, testset = train_test_split(data, test_size=.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "Computing the pearson_baseline similarity matrix...\n",
      "Done computing similarity matrix.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<surprise.prediction_algorithms.knns.KNNWithMeans at 0x7f54039f10b8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use user_based true/false to switch between user-based or item-based collaborative filtering\n",
    "algo = KNNWithMeans(k=50, sim_options={'name': 'pearson_baseline', 'user_based': False})\n",
    "algo.fit(trainset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# run the trained model against the testset\n",
    "test_pred = algo.test(testset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Prediction(uid='305', iid='175', r_ui=4.0, est=3.4368711608856324, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='279', iid='170', r_ui=3.0, est=3.9322523168295618, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='499', iid='166', r_ui=5.0, est=4.234057977298135, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='551', iid='660', r_ui=3.0, est=4.278039116829311, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='472', iid='257', r_ui=4.0, est=4.8307236523735, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='346', iid='660', r_ui=2.0, est=3.7237310828057573, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='250', iid='183', r_ui=4.0, est=4.03946541593474, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='933', iid='367', r_ui=4.0, est=2.4476810198452092, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='372', iid='201', r_ui=2.0, est=4.885223073744024, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='726', iid='248', r_ui=2.0, est=3.312073884131646, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='188', iid='1263', r_ui=3.0, est=2.969874188937135, details={'actual_k': 39, 'was_impossible': False}),\n",
       " Prediction(uid='883', iid='70', r_ui=3.0, est=3.771689785058765, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='527', iid='582', r_ui=2.0, est=3.4093735881812126, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='125', iid='122', r_ui=1.0, est=1.935349775750802, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='177', iid='121', r_ui=2.0, est=3.137610710935401, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='540', iid='274', r_ui=4.0, est=3.492085750536921, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='180', r_ui=5.0, est=4.350837569539941, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='621', iid='364', r_ui=3.0, est=2.9125780118326414, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='686', iid='48', r_ui=5.0, est=4.843502963768518, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='642', iid='742', r_ui=5.0, est=4.375078094558893, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='1124', r_ui=4.0, est=4.472472504752909, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='288', iid='173', r_ui=3.0, est=4.2184173980283, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='734', r_ui=1.0, est=2.5588897078794752, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='924', iid='433', r_ui=5.0, est=3.412346519526411, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='532', iid='761', r_ui=4.0, est=3.862719591980191, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='707', iid='367', r_ui=4.0, est=3.1831996580945656, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='1121', r_ui=4.0, est=4.167805381752792, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='489', iid='349', r_ui=4.0, est=3.626974934352593, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='618', iid='735', r_ui=3.0, est=3.557272194111026, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='682', iid='1478', r_ui=3.0, est=2.706602182041417, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='711', iid='111', r_ui=2.0, est=3.880683889195786, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='595', iid='472', r_ui=3.0, est=2.677086852951576, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='400', iid='286', r_ui=4.0, est=3.574176385471309, details={'actual_k': 7, 'was_impossible': False}),\n",
       " Prediction(uid='254', iid='151', r_ui=2.0, est=3.137630416554763, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='17', iid='150', r_ui=5.0, est=3.6241850561194418, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='435', iid='15', r_ui=3.0, est=3.548764866027852, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='49', iid='997', r_ui=1.0, est=2.3469849515707297, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='686', iid='1184', r_ui=1.0, est=3.461120679778273, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='300', iid='881', r_ui=5.0, est=3.8920276765887283, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='305', iid='61', r_ui=4.0, est=3.559353901142887, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='617', iid='7', r_ui=3.0, est=2.8460181590002547, details={'actual_k': 39, 'was_impossible': False}),\n",
       " Prediction(uid='543', iid='509', r_ui=3.0, est=3.808289889391359, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='682', iid='728', r_ui=3.0, est=2.7507754819148227, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='221', iid='156', r_ui=5.0, est=4.326949963892508, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='933', iid='95', r_ui=3.0, est=2.955977696189729, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='56', iid='173', r_ui=4.0, est=4.339255263221658, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='192', iid='277', r_ui=3.0, est=3.598246275822591, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='717', iid='299', r_ui=4.0, est=3.584145440869828, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='440', iid='313', r_ui=4.0, est=4.536786530373873, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='85', iid='443', r_ui=4.0, est=3.5226175192311184, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='1031', r_ui=2.0, est=2.8552385520748427, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='78', r_ui=2.0, est=2.9374065352437113, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='380', iid='529', r_ui=3.0, est=3.5770264756687236, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='880', iid='1277', r_ui=4.0, est=3.8319386066945555, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='796', iid='209', r_ui=3.0, est=3.669228947289686, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='194', r_ui=5.0, est=4.369055420383726, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='711', iid='408', r_ui=5.0, est=4.721493661716919, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='618', iid='660', r_ui=3.0, est=3.6039333666056814, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='79', r_ui=4.0, est=4.396886540584461, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='1274', r_ui=1.0, est=1.9867767963942817, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='174', r_ui=5.0, est=4.767490492768041, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='701', iid='300', r_ui=3.0, est=3.908144001602024, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='318', iid='892', r_ui=3.0, est=2.972955650835299, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='565', iid='638', r_ui=4.0, est=4.53715363459476, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='419', r_ui=3.0, est=3.8593752402422896, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='782', iid='1379', r_ui=3.0, est=2.212178150376601, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='601', iid='107', r_ui=4.0, est=2.9010335418276534, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='215', iid='98', r_ui=5.0, est=4.327995708587753, details={'actual_k': 39, 'was_impossible': False}),\n",
       " Prediction(uid='770', iid='294', r_ui=3.0, est=3.754719691290261, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='805', iid='33', r_ui=5.0, est=3.2073107438161825, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='414', iid='11', r_ui=5.0, est=4.447173362494505, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='677', iid='471', r_ui=4.0, est=4.235228965614097, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='339', iid='451', r_ui=3.0, est=3.5839027880777694, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='425', iid='1314', r_ui=3.0, est=1.893937023509237, details={'actual_k': 47, 'was_impossible': False}),\n",
       " Prediction(uid='113', iid='126', r_ui=5.0, est=4.336277571879182, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='391', iid='603', r_ui=5.0, est=4.443290900775992, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='354', r_ui=4.0, est=3.830188327977974, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='733', iid='130', r_ui=2.0, est=1.4060946412152906, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='91', iid='187', r_ui=5.0, est=4.203532094845178, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='358', iid='357', r_ui=4.0, est=3.6605702888687643, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='900', iid='589', r_ui=5.0, est=2.730577076431227, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='42', iid='194', r_ui=5.0, est=4.582264353849848, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='901', iid='22', r_ui=5.0, est=4.754613570921572, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='561', iid='597', r_ui=3.0, est=2.1972403856125493, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='755', iid='286', r_ui=5.0, est=3.0738541654040197, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='277', iid='591', r_ui=4.0, est=3.603873540556188, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='762', r_ui=4.0, est=3.422523171395732, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='523', iid='50', r_ui=5.0, est=5, details={'actual_k': 47, 'was_impossible': False}),\n",
       " Prediction(uid='920', iid='347', r_ui=4.0, est=3.0969653539715227, details={'actual_k': 8, 'was_impossible': False}),\n",
       " Prediction(uid='106', iid='165', r_ui=5.0, est=4.535566996811727, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='5', iid='447', r_ui=3.0, est=3.15743989280058, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='79', iid='246', r_ui=5.0, est=4.520402483964665, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='798', iid='1066', r_ui=2.0, est=3.090611976237558, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='391', iid='205', r_ui=5.0, est=3.856301690358882, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='878', iid='642', r_ui=3.0, est=2.9363524399494403, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='896', iid='1522', r_ui=2.0, est=1.9769284289897953, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='812', iid='328', r_ui=4.0, est=4.201795494548476, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='105', r_ui=1.0, est=1.4750885371806457, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='483', iid='582', r_ui=3.0, est=2.976379523119215, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='197', iid='344', r_ui=4.0, est=3.316794481217295, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='972', r_ui=1.0, est=1.7514835796392818, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='238', iid='300', r_ui=4.0, est=3.720139993053575, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='606', r_ui=5.0, est=4.512096231223586, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='40', iid='321', r_ui=4.0, est=2.6355779781854975, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='657', iid='269', r_ui=5.0, est=3.3861515671230835, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='1364', r_ui=1.0, est=3.5280705882352943, details={'was_impossible': True, 'reason': 'User and/or item is unkown.'}),\n",
       " Prediction(uid='91', iid='300', r_ui=4.0, est=3.954225664555894, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='497', iid='226', r_ui=3.0, est=3.343276935168098, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='664', iid='302', r_ui=4.0, est=4.353711765535252, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='394', iid='208', r_ui=5.0, est=4.507143364544546, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='173', iid='323', r_ui=5.0, est=3.8971233813268014, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='532', iid='470', r_ui=5.0, est=4.519876566320266, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='339', iid='650', r_ui=4.0, est=3.900352876334408, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='767', iid='659', r_ui=5.0, est=4.705131889284111, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='203', iid='282', r_ui=1.0, est=3.6969796198359077, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='379', iid='230', r_ui=4.0, est=3.777048651494364, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='694', iid='143', r_ui=4.0, est=4.197673953956993, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='23', iid='380', r_ui=5.0, est=3.120389317909668, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='337', iid='1133', r_ui=4.0, est=3.475767198117051, details={'actual_k': 7, 'was_impossible': False}),\n",
       " Prediction(uid='449', iid='748', r_ui=2.0, est=2.6531191915812977, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='591', iid='435', r_ui=4.0, est=3.930193140849228, details={'actual_k': 36, 'was_impossible': False}),\n",
       " Prediction(uid='23', iid='433', r_ui=5.0, est=3.776293555150851, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='1277', r_ui=2.0, est=2.3946987479666078, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='414', iid='301', r_ui=3.0, est=4.00361212063766, details={'actual_k': 14, 'was_impossible': False}),\n",
       " Prediction(uid='883', iid='81', r_ui=5.0, est=3.7655833109292542, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='11', iid='175', r_ui=3.0, est=3.6415009719273628, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='388', iid='307', r_ui=4.0, est=4.207095717942757, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='599', iid='278', r_ui=3.0, est=3.9750636012555844, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='78', iid='237', r_ui=5.0, est=3.8384266731771084, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='904', iid='216', r_ui=4.0, est=4.314102219278584, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='918', iid='1065', r_ui=4.0, est=3.0430186733508218, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='825', iid='864', r_ui=3.0, est=3.868899079586254, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='815', iid='174', r_ui=4.0, est=4.5771289430883675, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='385', iid='128', r_ui=5.0, est=3.045763956226766, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='497', iid='805', r_ui=3.0, est=3.4417708746569877, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='329', iid='512', r_ui=4.0, est=3.8452981665908834, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='136', iid='117', r_ui=4.0, est=3.5386805143812863, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='478', iid='160', r_ui=2.0, est=3.5445472583706756, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='215', iid='11', r_ui=2.0, est=3.6989533102960386, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='677', iid='289', r_ui=1.0, est=2.7275231737785472, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='657', iid='508', r_ui=4.0, est=3.711525438957988, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='345', iid='443', r_ui=5.0, est=3.872789859336257, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='413', iid='50', r_ui=5.0, est=4.510297352560994, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='174', iid='1139', r_ui=2.0, est=3.0281084666247313, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='896', iid='209', r_ui=3.0, est=3.6030030397149684, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='914', iid='371', r_ui=4.0, est=3.3268915050756096, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='177', iid='7', r_ui=4.0, est=3.733661952921916, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='764', iid='222', r_ui=4.0, est=3.908057419124449, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='801', iid='358', r_ui=4.0, est=3.539729445235964, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='798', iid='155', r_ui=3.0, est=3.196407373885121, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='462', r_ui=2.0, est=4.014371631312246, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='503', iid='58', r_ui=4.0, est=4.015604111789567, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='268', iid='472', r_ui=1.0, est=2.606480002881227, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='230', iid='25', r_ui=3.0, est=3.635884827553226, details={'actual_k': 40, 'was_impossible': False}),\n",
       " Prediction(uid='716', iid='605', r_ui=3.0, est=3.796368327586757, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='57', iid='294', r_ui=4.0, est=3.524834329777128, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='221', iid='154', r_ui=3.0, est=3.859625049853301, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='321', iid='463', r_ui=3.0, est=3.5887623962081596, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='56', iid='7', r_ui=5.0, est=4.0574195441414265, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='660', iid='121', r_ui=2.0, est=2.4971039608554397, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='471', iid='393', r_ui=5.0, est=3.364144199226148, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='90', iid='750', r_ui=4.0, est=4.284356112865201, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='688', iid='879', r_ui=5.0, est=4.705449710257025, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='761', iid='293', r_ui=4.0, est=3.105039744555796, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='201', iid='187', r_ui=3.0, est=3.9280592744630733, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='1', r_ui=4.0, est=4.228133477026473, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='772', r_ui=4.0, est=3.2607941013880137, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='663', r_ui=4.0, est=4.07996537647248, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='719', iid='285', r_ui=4.0, est=3.054149023939729, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='664', iid='230', r_ui=3.0, est=3.247796664342787, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='695', iid='300', r_ui=1.0, est=2.8906719181389753, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='406', iid='515', r_ui=2.0, est=4.166031820394828, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='458', iid='319', r_ui=4.0, est=3.1555298421329283, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='158', iid='39', r_ui=5.0, est=3.5382637106652726, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='846', iid='1066', r_ui=3.0, est=3.2491354028879993, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='927', iid='121', r_ui=5.0, est=4.047659270351178, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='1581', r_ui=1.0, est=3.5280705882352943, details={'was_impossible': True, 'reason': 'User and/or item is unkown.'}),\n",
       " Prediction(uid='234', iid='746', r_ui=2.0, est=2.94359666537313, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='293', iid='566', r_ui=3.0, est=2.873233460635909, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='593', iid='220', r_ui=3.0, est=3.4200168243889593, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='339', iid='213', r_ui=4.0, est=4.463598939693617, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='924', iid='277', r_ui=3.0, est=3.4133609923131303, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='393', iid='1225', r_ui=3.0, est=2.4101534556955047, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='189', iid='378', r_ui=4.0, est=4.271306106003188, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='535', iid='848', r_ui=3.0, est=3.4516620851168502, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='48', iid='524', r_ui=3.0, est=4.0082344197911715, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='463', iid='111', r_ui=2.0, est=3.2109547535084957, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='849', iid='27', r_ui=5.0, est=4.106992972241849, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='868', iid='198', r_ui=5.0, est=3.628573696400216, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='135', r_ui=3.0, est=3.656759585543214, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='716', iid='499', r_ui=4.0, est=4.466614950156553, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='593', iid='155', r_ui=5.0, est=3.6253213217632454, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='655', iid='692', r_ui=3.0, est=2.7671774655269035, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='825', iid='12', r_ui=5.0, est=4.463256321044766, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='271', iid='199', r_ui=4.0, est=4.177903407493959, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='314', iid='1220', r_ui=5.0, est=3.7702689344327585, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='399', iid='420', r_ui=3.0, est=2.9921111080865215, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='513', iid='252', r_ui=5.0, est=3.6915103576206922, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='432', iid='871', r_ui=2.0, est=2.6892654787859174, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='123', iid='14', r_ui=5.0, est=4.075193922759147, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='42', iid='1', r_ui=5.0, est=4.521719564613243, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='215', r_ui=4.0, est=3.6876446026591783, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='831', iid='358', r_ui=2.0, est=2.2903930312048457, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='293', iid='298', r_ui=4.0, est=3.116218516518763, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='685', r_ui=3.0, est=3.1628364988033337, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='516', r_ui=3.0, est=4.5397267102814665, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='532', iid='235', r_ui=3.0, est=3.4697730570934904, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='194', iid='514', r_ui=3.0, est=3.203455115574218, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='394', iid='179', r_ui=5.0, est=4.465276838172745, details={'actual_k': 40, 'was_impossible': False}),\n",
       " Prediction(uid='401', iid='481', r_ui=3.0, est=3.19211093420138, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='868', iid='843', r_ui=1.0, est=2.462721626732604, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='889', iid='944', r_ui=3.0, est=3.0171180314455457, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='135', iid='227', r_ui=3.0, est=3.1590413067719307, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='625', r_ui=3.0, est=3.158405128292275, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='334', iid='607', r_ui=3.0, est=3.8159358460046167, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='299', iid='115', r_ui=3.0, est=3.644635172972174, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='581', r_ui=4.0, est=3.3291373135862807, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='456', iid='963', r_ui=4.0, est=4.2407304011892535, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='864', iid='66', r_ui=3.0, est=3.8732863838104974, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='447', iid='471', r_ui=4.0, est=3.7329727419107646, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='481', iid='1089', r_ui=3.0, est=2.8177323661479408, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='17', iid='269', r_ui=4.0, est=3.166538596030975, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='786', iid='376', r_ui=3.0, est=3.142208163309555, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='121', iid='742', r_ui=5.0, est=2.968604562641304, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='263', iid='419', r_ui=5.0, est=4.0365444322548685, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='867', iid='175', r_ui=5.0, est=4.179580952343176, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='472', iid='2', r_ui=5.0, est=4.220183243050075, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='328', iid='579', r_ui=3.0, est=2.7509639335052354, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='379', iid='12', r_ui=5.0, est=4.818456200958608, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='588', iid='29', r_ui=3.0, est=3.0158853381107154, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='339', iid='258', r_ui=3.0, est=4.00258526550487, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='133', r_ui=5.0, est=3.95481579166786, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='201', iid='568', r_ui=3.0, est=2.9471274702684096, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='456', iid='86', r_ui=2.0, est=3.7231935832642296, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='94', iid='313', r_ui=4.0, est=4.45500672880259, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='464', iid='479', r_ui=4.0, est=4.9016133099419426, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='149', r_ui=4.0, est=3.816160661758854, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='407', iid='1160', r_ui=1.0, est=3.4153149742613915, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='330', iid='732', r_ui=5.0, est=4.689067564466387, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='527', iid='507', r_ui=5.0, est=3.75640703796969, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='180', iid='111', r_ui=5.0, est=3.8138456729215187, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='94', iid='410', r_ui=4.0, est=3.558215167354566, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='207', iid='1098', r_ui=4.0, est=3.2314636992151726, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='881', iid='554', r_ui=1.0, est=3.1058999009476578, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='119', iid='313', r_ui=5.0, est=4.8072930813944135, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='176', iid='340', r_ui=5.0, est=3.925120564662323, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='44', iid='204', r_ui=4.0, est=3.8900266297206025, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='919', iid='118', r_ui=4.0, est=3.2025968900559505, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='674', iid='304', r_ui=3.0, est=4.037497438925728, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='666', iid='286', r_ui=5.0, est=3.666600827325762, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='433', iid='748', r_ui=4.0, est=2.5198392964473544, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='518', r_ui=5.0, est=4.364408335738318, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='22', iid='53', r_ui=3.0, est=2.7657366655432836, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='298', iid='546', r_ui=3.0, est=3.3861342506839907, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='100', iid='323', r_ui=3.0, est=3.0120421853946158, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='58', iid='13', r_ui=3.0, est=3.590324520774768, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='524', iid='582', r_ui=3.0, est=3.7415701262036305, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='966', r_ui=4.0, est=4.581660500027462, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='13', iid='271', r_ui=1.0, est=2.878292756197303, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='137', iid='181', r_ui=5.0, est=4.786039814833424, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='453', iid='164', r_ui=3.0, est=3.4267786357895034, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='868', iid='183', r_ui=5.0, est=3.776868442983987, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='896', iid='820', r_ui=2.0, est=2.306258842871425, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='291', iid='144', r_ui=5.0, est=4.305387747545042, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='474', iid='603', r_ui=5.0, est=4.6897117150241305, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='311', iid='117', r_ui=4.0, est=4.143077367611788, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='676', iid='539', r_ui=4.0, est=2.4958793549367075, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='460', iid='297', r_ui=3.0, est=3.8503925662508474, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='803', iid='338', r_ui=2.0, est=1.7813586730444748, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='684', iid='121', r_ui=3.0, est=3.64969283901085, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='330', iid='118', r_ui=5.0, est=4.190809185711743, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='279', iid='216', r_ui=3.0, est=3.4452112190694573, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='385', r_ui=4.0, est=3.366532132231648, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='790', iid='742', r_ui=4.0, est=3.367476394610293, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='671', iid='810', r_ui=2.0, est=3.3464321526743253, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='650', iid='521', r_ui=3.0, est=3.2602433043854124, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='156', iid='48', r_ui=4.0, est=3.970342568566844, details={'actual_k': 19, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='156', r_ui=3.0, est=4.156239953390576, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='993', r_ui=3.0, est=3.367228725660329, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='13', iid='33', r_ui=5.0, est=3.129187161925646, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='771', iid='50', r_ui=4.0, est=4.304103256203624, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='451', iid='286', r_ui=1.0, est=3.3003529266555156, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='334', iid='14', r_ui=3.0, est=3.9065892548335936, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='16', iid='385', r_ui=5.0, est=4.426422844729235, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='472', iid='181', r_ui=5.0, est=4.93848043638041, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='788', iid='192', r_ui=4.0, est=3.7285693346215023, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='596', r_ui=2.0, est=3.5029854987781346, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='731', iid='1', r_ui=2.0, est=3.6903658067041984, details={'actual_k': 44, 'was_impossible': False}),\n",
       " Prediction(uid='630', iid='983', r_ui=3.0, est=2.4335833418420827, details={'actual_k': 39, 'was_impossible': False}),\n",
       " Prediction(uid='804', iid='243', r_ui=3.0, est=2.9929282252421134, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='851', iid='272', r_ui=5.0, est=4.424170560143826, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='938', iid='508', r_ui=4.0, est=3.7729681603399663, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='504', iid='440', r_ui=3.0, est=1.6915994604012585, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='190', iid='544', r_ui=4.0, est=3.062982413203984, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='657', iid='327', r_ui=1.0, est=3.8465134722748755, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='655', iid='1024', r_ui=3.0, est=2.858207580693587, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='716', iid='102', r_ui=2.0, est=3.455476472225689, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='194', iid='7', r_ui=3.0, est=3.2475647829840173, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='44', iid='717', r_ui=3.0, est=2.820071058459611, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='877', iid='70', r_ui=5.0, est=3.69679651253, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='497', iid='83', r_ui=2.0, est=3.791611755986108, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='883', iid='1005', r_ui=5.0, est=4.118843123033506, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='228', iid='98', r_ui=3.0, est=3.803884480065202, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='189', iid='1404', r_ui=5.0, est=3.1398478496703497, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='889', iid='493', r_ui=3.0, est=3.870725053210239, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='396', iid='840', r_ui=3.0, est=2.9244817396271787, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='874', iid='125', r_ui=3.0, est=3.2287288785262263, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='905', iid='125', r_ui=3.0, est=3.2986230961467893, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='8', r_ui=4.0, est=3.6452922613834624, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='343', iid='159', r_ui=2.0, est=3.4156870175368907, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='73', r_ui=2.0, est=3.003322392217798, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='383', r_ui=2.0, est=2.482805904953466, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='378', iid='569', r_ui=3.0, est=2.4897990212915198, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='222', iid='391', r_ui=3.0, est=2.612338057401356, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='618', iid='176', r_ui=4.0, est=3.7095731169291577, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='933', r_ui=2.0, est=2.2191013335631995, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='607', r_ui=3.0, est=3.8420555628954474, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='458', r_ui=3.0, est=3.2113048124790677, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='753', iid='427', r_ui=5.0, est=3.7211982280020504, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='162', iid='11', r_ui=4.0, est=3.731948400858421, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='559', r_ui=3.0, est=3.233307129308992, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='44', iid='176', r_ui=5.0, est=4.047086907912646, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='325', iid='521', r_ui=4.0, est=3.50204665930761, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='681', iid='1394', r_ui=5.0, est=3.376777165927769, details={'actual_k': 2, 'was_impossible': False}),\n",
       " Prediction(uid='790', iid='65', r_ui=4.0, est=3.0893271647795526, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='566', iid='135', r_ui=5.0, est=3.9479598502931865, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='731', iid='136', r_ui=4.0, est=4.05303473218309, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='250', iid='596', r_ui=5.0, est=3.6503531963779383, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='574', iid='305', r_ui=3.0, est=3.5381415502212805, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='707', iid='936', r_ui=4.0, est=4.069397697654518, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='213', iid='79', r_ui=5.0, est=4.511224633764155, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='358', iid='179', r_ui=4.0, est=3.7751167022547647, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='432', r_ui=3.0, est=3.9924387395431946, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='593', iid='211', r_ui=4.0, est=4.022376842074949, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='668', iid='137', r_ui=3.0, est=3.8776705833050005, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='201', iid='454', r_ui=2.0, est=2.335370981840843, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='311', iid='654', r_ui=3.0, est=4.197406822858861, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='500', iid='268', r_ui=5.0, est=3.9808072036121134, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='625', r_ui=4.0, est=3.617423401981395, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='815', iid='176', r_ui=4.0, est=4.238953703164396, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='591', r_ui=5.0, est=3.871257886503848, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='1178', r_ui=1.0, est=2.048244699178848, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='200', iid='692', r_ui=3.0, est=4.43246031219166, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='18', iid='408', r_ui=5.0, est=4.5617751281766745, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='83', iid='95', r_ui=4.0, est=4.295575907760155, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='223', r_ui=4.0, est=4.448936348827726, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='711', iid='202', r_ui=4.0, est=3.8612594999572307, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='588', iid='100', r_ui=1.0, est=4.15134376212671, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='188', iid='211', r_ui=4.0, est=4.017522713769628, details={'actual_k': 41, 'was_impossible': False}),\n",
       " Prediction(uid='914', iid='732', r_ui=2.0, est=3.3979830280460868, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='707', iid='347', r_ui=5.0, est=3.4741046695554054, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='119', iid='1052', r_ui=4.0, est=3.0851740705893924, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='693', iid='300', r_ui=2.0, est=3.2080206445072457, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='426', iid='526', r_ui=4.0, est=3.8014576132080022, details={'actual_k': 46, 'was_impossible': False}),\n",
       " Prediction(uid='642', iid='1047', r_ui=3.0, est=3.6570733945356877, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='82', iid='504', r_ui=4.0, est=3.3915595104074754, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='224', iid='555', r_ui=3.0, est=1.7187027837946676, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='299', iid='319', r_ui=3.0, est=3.131198192773301, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='735', r_ui=4.0, est=3.708178273901481, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='376', iid='223', r_ui=4.0, est=4.1652648641521495, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='378', iid='732', r_ui=4.0, est=3.709958727697639, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='327', iid='960', r_ui=5.0, est=2.8692263900577086, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='790', iid='83', r_ui=3.0, est=3.514367410055575, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='400', iid='332', r_ui=2.0, est=3.6295157207102946, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='21', iid='292', r_ui=3.0, est=3.334407974312649, details={'actual_k': 44, 'was_impossible': False}),\n",
       " Prediction(uid='723', iid='50', r_ui=4.0, est=3.8967734520504793, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='773', iid='386', r_ui=3.0, est=2.3969146635145275, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='500', iid='143', r_ui=3.0, est=3.229047486274787, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='932', iid='663', r_ui=4.0, est=4.245668427758631, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='346', iid='237', r_ui=4.0, est=3.814463622555453, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='6', iid='470', r_ui=3.0, est=3.157965451489852, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='834', iid='237', r_ui=5.0, est=3.7987899295832044, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='733', iid='922', r_ui=3.0, est=3.178882586710375, details={'actual_k': 46, 'was_impossible': False}),\n",
       " Prediction(uid='286', iid='428', r_ui=5.0, est=3.878825641758147, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='587', iid='347', r_ui=3.0, est=3.2994390170364305, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='577', iid='241', r_ui=5.0, est=3.965636945727655, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='802', iid='327', r_ui=2.0, est=3.846438562495194, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='32', iid='122', r_ui=2.0, est=2.603750829460397, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='844', iid='549', r_ui=3.0, est=3.1912324852956218, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='617', iid='294', r_ui=1.0, est=1.570047457534896, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='758', iid='448', r_ui=4.0, est=3.60837980411962, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='551', iid='282', r_ui=5.0, est=4.395866857546689, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='452', iid='23', r_ui=2.0, est=3.696366845843784, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='385', r_ui=4.0, est=3.0056001885454675, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='988', r_ui=2.0, est=1.1456851004874498, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='467', iid='269', r_ui=4.0, est=4.115758544497064, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='7', r_ui=4.0, est=3.5664379313011114, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='122', iid='513', r_ui=4.0, est=4.554300005949336, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='336', iid='577', r_ui=1.0, est=2.1120474026479, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='414', r_ui=4.0, est=3.7260419533689917, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='503', iid='241', r_ui=5.0, est=3.7681555759185725, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='94', iid='474', r_ui=5.0, est=4.737886373596323, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='263', iid='523', r_ui=5.0, est=4.235160559804756, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='930', iid='286', r_ui=3.0, est=3.132856062302533, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='249', iid='147', r_ui=5.0, est=3.6652911498719463, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='901', iid='204', r_ui=5.0, est=4.454373549677321, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='174', iid='721', r_ui=2.0, est=3.2988745849115664, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='374', iid='168', r_ui=1.0, est=3.5755149874454553, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='848', iid='154', r_ui=5.0, est=4.011862011521348, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='327', iid='230', r_ui=4.0, est=2.8155028381736233, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='45', iid='1', r_ui=5.0, est=4.29430196158436, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='291', iid='240', r_ui=4.0, est=3.4936868392263007, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='591', iid='172', r_ui=3.0, est=3.899160031244431, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='23', iid='73', r_ui=3.0, est=3.1398861753165535, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='851', iid='1675', r_ui=3.0, est=3.5280705882352943, details={'was_impossible': True, 'reason': 'User and/or item is unkown.'}),\n",
       " Prediction(uid='331', iid='467', r_ui=3.0, est=3.28568843998626, details={'actual_k': 36, 'was_impossible': False}),\n",
       " Prediction(uid='145', iid='316', r_ui=5.0, est=4.588699555054784, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='524', iid='612', r_ui=3.0, est=3.638293308127218, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='673', iid='322', r_ui=4.0, est=3.2141563703558202, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='425', iid='89', r_ui=4.0, est=3.9587868116855116, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='191', iid='315', r_ui=5.0, est=4.373482486368113, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='650', iid='160', r_ui=3.0, est=3.2041946446925413, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='322', iid='603', r_ui=5.0, est=4.638753214142106, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='916', iid='148', r_ui=2.0, est=2.609544787839217, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='796', r_ui=4.0, est=3.176284258226928, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='522', iid='205', r_ui=4.0, est=4.243817081923336, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='280', iid='742', r_ui=4.0, est=3.4058486242506714, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='853', iid='887', r_ui=2.0, est=4.262177501139092, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='805', iid='179', r_ui=4.0, est=4.245141345401841, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='842', iid='288', r_ui=3.0, est=3.5914267718404624, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='943', iid='576', r_ui=4.0, est=2.720889934721909, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='772', iid='300', r_ui=4.0, est=4.331214586412935, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='328', iid='176', r_ui=5.0, est=3.9421519652921817, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='825', iid='1008', r_ui=1.0, est=3.6170219991214343, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='334', iid='856', r_ui=4.0, est=3.861770505699803, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='198', r_ui=4.0, est=3.8914282393544544, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='795', iid='826', r_ui=3.0, est=2.1023360938784412, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='551', iid='591', r_ui=5.0, est=4.213515928812353, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='213', iid='133', r_ui=3.0, est=4.586763604436795, details={'actual_k': 46, 'was_impossible': False}),\n",
       " Prediction(uid='790', iid='427', r_ui=4.0, est=3.883693777462332, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='299', iid='515', r_ui=4.0, est=3.988689352691135, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='332', iid='342', r_ui=4.0, est=3.7684438753738383, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='916', iid='229', r_ui=3.0, est=2.666943543827819, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='551', iid='721', r_ui=5.0, est=3.691025660265064, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='64', iid='202', r_ui=4.0, est=3.720919738855558, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='758', iid='319', r_ui=4.0, est=3.70269119348293, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='167', iid='674', r_ui=2.0, est=2.823759022516428, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='85', iid='526', r_ui=4.0, est=3.685667468476884, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='392', iid='493', r_ui=4.0, est=4.752482242184712, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='15', r_ui=5.0, est=3.959878772124477, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='542', iid='196', r_ui=4.0, est=3.7103558197928175, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='269', iid='474', r_ui=4.0, est=4.356956152910047, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='90', iid='739', r_ui=5.0, est=3.853814979517863, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='796', iid='294', r_ui=3.0, est=3.675298576573576, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='585', iid='1485', r_ui=3.0, est=2.3671937256557896, details={'actual_k': 4, 'was_impossible': False}),\n",
       " Prediction(uid='16', iid='467', r_ui=5.0, est=4.550551921469898, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='1210', r_ui=1.0, est=2.6775071247757545, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='737', iid='196', r_ui=3.0, est=3.83756124165128, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='180', iid='694', r_ui=5.0, est=4.819337619392725, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='664', iid='134', r_ui=5.0, est=4.541554412393919, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='445', iid='221', r_ui=1.0, est=2.5717733733287673, details={'actual_k': 47, 'was_impossible': False}),\n",
       " Prediction(uid='709', iid='28', r_ui=5.0, est=3.97184453869872, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='332', iid='840', r_ui=4.0, est=3.4073534558381287, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='648', iid='722', r_ui=3.0, est=2.706506175523024, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='823', iid='187', r_ui=5.0, est=4.673575502174771, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='233', iid='483', r_ui=5.0, est=4.920455830455543, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='221', iid='1217', r_ui=4.0, est=2.858646043782646, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='601', iid='288', r_ui=1.0, est=2.909694199873799, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='31', iid='32', r_ui=5.0, est=3.9811707575204185, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='67', r_ui=3.0, est=3.36062294672144, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='537', iid='732', r_ui=3.0, est=2.5318248806907286, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='463', iid='1060', r_ui=2.0, est=2.731812482611002, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='652', r_ui=4.0, est=3.7875687224922983, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='248', r_ui=1.0, est=3.742012910703714, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='98', iid='210', r_ui=4.0, est=3.59443513518467, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='521', iid='833', r_ui=2.0, est=2.9141013667175737, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='162', iid='230', r_ui=2.0, est=3.5622756962910165, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='599', iid='1', r_ui=4.0, est=4.723663857340821, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='866', r_ui=2.0, est=3.431744531983985, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='622', iid='230', r_ui=3.0, est=3.6236661795910585, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='230', iid='405', r_ui=4.0, est=3.725588803271487, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='495', iid='684', r_ui=5.0, est=4.375801821982468, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='186', iid='281', r_ui=4.0, est=3.3453948612700217, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='97', r_ui=4.0, est=3.7721139333710076, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='469', iid='194', r_ui=5.0, est=4.558042518213319, details={'actual_k': 19, 'was_impossible': False}),\n",
       " Prediction(uid='207', iid='210', r_ui=3.0, est=3.5642559740575024, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='83', iid='121', r_ui=4.0, est=4.002660538050661, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='416', iid='571', r_ui=3.0, est=2.917759898778633, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='617', iid='1019', r_ui=4.0, est=3.4577674992392953, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='294', iid='1', r_ui=5.0, est=4.13327443849044, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='398', iid='173', r_ui=4.0, est=4.318405023489565, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='311', iid='431', r_ui=4.0, est=3.779025166560977, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='316', r_ui=4.0, est=4.543096942476355, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='545', iid='202', r_ui=4.0, est=3.7052498105942617, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='99', iid='107', r_ui=3.0, est=3.497324865262032, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='621', iid='270', r_ui=4.0, est=4.071633818685417, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='766', iid='514', r_ui=4.0, est=3.581791375175913, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='85', iid='432', r_ui=4.0, est=3.7878473954075287, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='875', iid='321', r_ui=3.0, est=3.434518476801654, details={'actual_k': 36, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='761', r_ui=1.0, est=2.3465746303186306, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='149', iid='896', r_ui=4.0, est=3.390411999466465, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='798', iid='690', r_ui=4.0, est=3.5174550852667736, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='756', iid='588', r_ui=4.0, est=3.4763892333951363, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='454', iid='8', r_ui=5.0, est=3.407636316417584, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='592', iid='147', r_ui=4.0, est=3.591931132528285, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='579', iid='709', r_ui=5.0, est=3.8147109232013787, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='883', iid='382', r_ui=3.0, est=3.8911704634537427, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='374', iid='200', r_ui=5.0, est=3.332435606203184, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='473', r_ui=3.0, est=3.055107967877569, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='223', r_ui=5.0, est=3.902825575229478, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='684', r_ui=5.0, est=4.246995970538944, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='585', iid='165', r_ui=4.0, est=4.066877323260979, details={'actual_k': 36, 'was_impossible': False}),\n",
       " Prediction(uid='546', iid='895', r_ui=3.0, est=3.7384226531079405, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='339', iid='154', r_ui=4.0, est=4.221759014980408, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='154', iid='324', r_ui=2.0, est=2.929997532450397, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='40', iid='340', r_ui=2.0, est=2.5929308228399477, details={'actual_k': 14, 'was_impossible': False}),\n",
       " Prediction(uid='379', iid='433', r_ui=4.0, est=4.087979568467626, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='126', iid='326', r_ui=2.0, est=3.4241555906587386, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='423', iid='272', r_ui=5.0, est=4.2289067871399935, details={'actual_k': 34, 'was_impossible': False}),\n",
       " Prediction(uid='297', iid='1217', r_ui=1.0, est=2.6213553705963424, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='256', iid='294', r_ui=3.0, est=3.9791548761850293, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='362', iid='350', r_ui=5.0, est=3.9768744753907725, details={'actual_k': 7, 'was_impossible': False}),\n",
       " Prediction(uid='736', iid='181', r_ui=2.0, est=3.145610441287197, details={'actual_k': 8, 'was_impossible': False}),\n",
       " Prediction(uid='145', iid='202', r_ui=4.0, est=3.9984403476081694, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='250', iid='56', r_ui=4.0, est=4.35336754433239, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='318', iid='289', r_ui=3.0, est=3.4305240695573556, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='521', iid='427', r_ui=3.0, est=3.5970317843025676, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='669', iid='348', r_ui=1.0, est=2.6954207417402998, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='711', iid='727', r_ui=4.0, est=3.9829447585516307, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='343', iid='408', r_ui=5.0, est=5, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='291', iid='1028', r_ui=3.0, est=3.3523205964851917, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='911', iid='151', r_ui=5.0, est=3.7323026650946436, details={'actual_k': 46, 'was_impossible': False}),\n",
       " Prediction(uid='313', iid='486', r_ui=3.0, est=3.8798640663703914, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='381', iid='607', r_ui=4.0, est=4.2048765408382875, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='379', iid='271', r_ui=3.0, est=3.400676882365044, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='897', iid='684', r_ui=2.0, est=4.180885666839323, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='295', r_ui=2.0, est=3.1420306526592796, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='864', iid='58', r_ui=5.0, est=4.144723507305236, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='655', iid='796', r_ui=2.0, est=2.221139286968051, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='458', iid='56', r_ui=5.0, est=4.145514864273775, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='104', iid='751', r_ui=4.0, est=2.7827884364733904, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='10', r_ui=5.0, est=4.228579340702458, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='107', r_ui=4.0, est=3.3221565550760843, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='38', iid='35', r_ui=5.0, est=2.97267881391073, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='871', iid='352', r_ui=3.0, est=2.02698133754631, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='804', iid='133', r_ui=3.0, est=4.002157398542791, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='875', iid='32', r_ui=5.0, est=4.136951191547332, details={'actual_k': 34, 'was_impossible': False}),\n",
       " Prediction(uid='330', iid='763', r_ui=5.0, est=4.017547591138074, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='978', r_ui=2.0, est=2.8897679195929546, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='899', iid='157', r_ui=4.0, est=3.3728090848725554, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='408', r_ui=5.0, est=4.56637227942005, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='346', iid='144', r_ui=4.0, est=4.077571049250783, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='455', iid='234', r_ui=4.0, est=3.626001635140312, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='763', iid='209', r_ui=4.0, est=4.153440295003008, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='498', iid='180', r_ui=4.0, est=3.811802795238071, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='178', r_ui=4.0, est=4.331011044232905, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='782', iid='315', r_ui=4.0, est=3.835840190638155, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='250', r_ui=4.0, est=3.4610504343951947, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='655', iid='176', r_ui=2.0, est=3.1998416786547956, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='421', iid='200', r_ui=3.0, est=3.9108996255810426, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='500', iid='476', r_ui=2.0, est=2.581945341226845, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='774', iid='202', r_ui=5.0, est=2.410938986279697, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='561', iid='171', r_ui=5.0, est=3.3742372383860193, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='296', iid='289', r_ui=3.0, est=3.3718152918381183, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='385', iid='485', r_ui=4.0, est=2.9404278057992026, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='770', iid='325', r_ui=4.0, est=3.5273614664379114, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='707', iid='723', r_ui=3.0, est=3.1278452071580336, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='380', iid='1113', r_ui=4.0, est=2.5332352665099362, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='683', iid='187', r_ui=5.0, est=4.24672237001367, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='645', iid='70', r_ui=4.0, est=3.7635796585068704, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='921', r_ui=4.0, est=4.039755648728042, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='660', iid='183', r_ui=2.0, est=3.465625877955137, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='863', iid='262', r_ui=3.0, est=3.5108857257254527, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='686', r_ui=4.0, est=3.5337495301070265, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='331', iid='302', r_ui=5.0, est=4.043654380658828, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='78', iid='1160', r_ui=5.0, est=2.8643827976036964, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='624', iid='741', r_ui=4.0, est=3.5534007537096994, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='560', iid='496', r_ui=3.0, est=3.760177793984022, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='782', iid='361', r_ui=3.0, est=3.145716848817275, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='84', iid='64', r_ui=5.0, est=4.525479985456527, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='609', iid='1', r_ui=1.0, est=3.2657817673676646, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='378', iid='181', r_ui=4.0, est=3.9618707101106634, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='303', iid='395', r_ui=2.0, est=2.7383611615633594, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='833', iid='106', r_ui=2.0, est=2.2344158661828817, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='238', iid='471', r_ui=4.0, est=3.6458797447490117, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='189', iid='952', r_ui=5.0, est=3.316045939330942, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='541', iid='95', r_ui=4.0, est=4.213226100260736, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='135', iid='39', r_ui=3.0, est=3.1164084265061867, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='618', iid='4', r_ui=2.0, est=3.2555886766164632, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='576', iid='204', r_ui=4.0, est=3.7083525492419565, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='286', iid='95', r_ui=5.0, est=3.9324689694255794, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='467', iid='50', r_ui=4.0, est=4.326177747580362, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='422', iid='299', r_ui=1.0, est=2.844225435538809, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='757', iid='257', r_ui=4.0, est=3.5644392339422715, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='448', r_ui=4.0, est=3.7303791087065576, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='930', iid='14', r_ui=4.0, est=2.978800471308145, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='283', iid='202', r_ui=5.0, est=4.247551117856151, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='551', iid='343', r_ui=4.0, est=3.4174503151113984, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='504', iid='705', r_ui=4.0, est=3.9140734897800105, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='705', iid='226', r_ui=3.0, est=3.68459007495859, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='504', r_ui=5.0, est=4.173915433110103, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='340', iid='486', r_ui=4.0, est=4.400280974542719, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='59', iid='644', r_ui=4.0, est=4.0693511019392865, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='476', iid='88', r_ui=4.0, est=3.5928440041421794, details={'actual_k': 46, 'was_impossible': False}),\n",
       " Prediction(uid='407', iid='231', r_ui=3.0, est=2.738154287903547, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='1435', r_ui=4.0, est=2.755036529929068, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='816', iid='332', r_ui=4.0, est=4.1880188581962665, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='270', iid='596', r_ui=5.0, est=3.749632343046031, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='52', iid='19', r_ui=5.0, est=4.491429516682328, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='757', iid='181', r_ui=3.0, est=3.9290680974696928, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='867', iid='748', r_ui=4.0, est=3.52563057247632, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='943', iid='96', r_ui=4.0, est=4.027999281318092, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='181', r_ui=5.0, est=3.5881121362538453, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='353', iid='898', r_ui=2.0, est=3.401694614951761, details={'actual_k': 4, 'was_impossible': False}),\n",
       " Prediction(uid='345', iid='736', r_ui=3.0, est=4.07306114636986, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='922', iid='56', r_ui=1.0, est=3.8845353943167953, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='239', iid='482', r_ui=3.0, est=4.454609330109894, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='396', r_ui=4.0, est=2.990445800394988, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='83', iid='28', r_ui=4.0, est=4.506494871862982, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='198', iid='184', r_ui=3.0, est=3.0966703495821806, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='351', iid='289', r_ui=5.0, est=3.850411525471612, details={'actual_k': 19, 'was_impossible': False}),\n",
       " Prediction(uid='893', iid='288', r_ui=3.0, est=3.7195440605616015, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='49', iid='1072', r_ui=1.0, est=2.1037336107362776, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='311', iid='125', r_ui=4.0, est=4.078850117502503, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='451', iid='1295', r_ui=2.0, est=2.322850929760458, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='693', iid='199', r_ui=3.0, est=3.290244133192222, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='330', iid='102', r_ui=4.0, est=4.188892480068719, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='234', iid='5', r_ui=3.0, est=2.6831441398870055, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='72', iid='56', r_ui=5.0, est=4.125557526915989, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='81', iid='476', r_ui=2.0, est=2.8406314276270033, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='372', iid='176', r_ui=3.0, est=5, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='619', iid='562', r_ui=3.0, est=3.6004291276111484, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='270', iid='286', r_ui=5.0, est=4.72016403054703, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='187', iid='651', r_ui=5.0, est=3.8254935228654663, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='265', iid='240', r_ui=3.0, est=2.5446170749622072, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='168', r_ui=4.0, est=4.112391062745582, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='399', iid='63', r_ui=3.0, est=2.627527097918801, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='277', r_ui=4.0, est=3.510272308070245, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='660', r_ui=5.0, est=3.8657214237592856, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='217', iid='391', r_ui=4.0, est=2.3767075377899083, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='689', iid='410', r_ui=1.0, est=3.6847312011630047, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='497', iid='38', r_ui=3.0, est=2.94888707489074, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='938', iid='1047', r_ui=3.0, est=2.7671630146902735, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='331', iid='277', r_ui=4.0, est=3.4497311202648158, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='500', iid='639', r_ui=4.0, est=3.6786080980134406, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='419', iid='1451', r_ui=4.0, est=4.0196385092085185, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='472', iid='362', r_ui=5.0, est=3.750046577482472, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='163', iid='28', r_ui=3.0, est=3.5399946487129865, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='732', iid='305', r_ui=2.0, est=4.758762062491539, details={'actual_k': 7, 'was_impossible': False}),\n",
       " Prediction(uid='456', iid='550', r_ui=2.0, est=2.821350479651075, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='484', iid='210', r_ui=5.0, est=4.544164100067322, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='896', iid='172', r_ui=5.0, est=4.517812741598985, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='7', iid='396', r_ui=4.0, est=3.3610968485326147, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='16', iid='629', r_ui=4.0, est=4.034168979156869, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='537', iid='486', r_ui=3.0, est=3.14886635977097, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='828', iid='316', r_ui=5.0, est=3.225998341866204, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='260', iid='990', r_ui=5.0, est=3.329966093670989, details={'actual_k': 7, 'was_impossible': False}),\n",
       " Prediction(uid='256', iid='282', r_ui=3.0, est=4.637180481890649, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='885', iid='420', r_ui=4.0, est=3.395798103700519, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='174', iid='655', r_ui=5.0, est=4.1417057008369405, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='798', iid='132', r_ui=4.0, est=3.7409793726727347, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='807', iid='605', r_ui=3.0, est=3.6697539885777286, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='399', iid='47', r_ui=3.0, est=2.8599671353700464, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='201', iid='1065', r_ui=3.0, est=2.991010090073235, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='444', iid='912', r_ui=4.0, est=2.8384674085872303, details={'actual_k': 6, 'was_impossible': False}),\n",
       " Prediction(uid='842', iid='302', r_ui=5.0, est=4.560507726367257, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='733', iid='1114', r_ui=3.0, est=2.9733205698288523, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='207', iid='763', r_ui=3.0, est=3.033455387404623, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='862', iid='258', r_ui=5.0, est=4.513608823663179, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='931', iid='125', r_ui=4.0, est=3.67179931129002, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='435', iid='890', r_ui=1.0, est=2.0804752587190807, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='468', iid='173', r_ui=5.0, est=4.540510410647034, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='654', iid='1285', r_ui=4.0, est=3.3434308272018503, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='413', iid='284', r_ui=4.0, est=3.1818697206512616, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='97', iid='195', r_ui=5.0, est=4.260912757759474, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='95', iid='423', r_ui=5.0, est=4.017962927167456, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='805', iid='761', r_ui=3.0, est=2.8509791345087834, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='9', r_ui=2.0, est=3.877225379517258, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='868', iid='189', r_ui=5.0, est=3.4674958388071713, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='671', iid='31', r_ui=2.0, est=3.8842399251723996, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='193', iid='1', r_ui=4.0, est=3.554613111512995, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='889', iid='1139', r_ui=1.0, est=2.5983862892022884, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='472', iid='222', r_ui=5.0, est=4.7654037062352215, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='11', iid='726', r_ui=3.0, est=2.127684636504579, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='256', iid='288', r_ui=5.0, est=4.011311689033674, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='194', iid='230', r_ui=1.0, est=2.5193105709982673, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='328', iid='300', r_ui=5.0, est=3.743040947194485, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='500', iid='202', r_ui=4.0, est=3.3405451291538895, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='7', iid='448', r_ui=3.0, est=3.9615057462385086, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='933', iid='98', r_ui=5.0, est=3.447115128876856, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='853', iid='332', r_ui=3.0, est=3.2952786552598057, details={'actual_k': 27, 'was_impossible': False}),\n",
       " Prediction(uid='47', iid='307', r_ui=4.0, est=3.670581603856617, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='21', iid='325', r_ui=4.0, est=2.21284323568293, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='660', iid='243', r_ui=2.0, est=1.6932193621029987, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='128', iid='88', r_ui=4.0, est=3.6422673076400893, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='751', iid='196', r_ui=4.0, est=3.828737311802852, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='831', iid='1', r_ui=4.0, est=4.0344557742370775, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='537', iid='97', r_ui=2.0, est=2.797068527040151, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='458', iid='1011', r_ui=3.0, est=3.319049813525159, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='880', iid='56', r_ui=5.0, est=4.518166261590657, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='293', iid='48', r_ui=5.0, est=3.814112378669578, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='18', iid='234', r_ui=3.0, est=3.7096803464950967, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='763', iid='1098', r_ui=3.0, est=3.869133682022775, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='406', iid='86', r_ui=4.0, est=3.916126298357662, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='738', iid='252', r_ui=4.0, est=2.9506509788504176, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='210', iid='96', r_ui=4.0, est=4.522599015868748, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='346', iid='210', r_ui=4.0, est=3.994388612801132, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='290', iid='153', r_ui=3.0, est=3.527160219931449, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='89', iid='283', r_ui=4.0, est=4.241338144730471, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='366', r_ui=2.0, est=2.5939115048520476, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='942', iid='1204', r_ui=4.0, est=4.12020090148859, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='56', iid='31', r_ui=4.0, est=3.985791905936233, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='303', iid='239', r_ui=3.0, est=3.659442323128412, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='200', iid='68', r_ui=5.0, est=4.03662297154599, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='506', iid='95', r_ui=5.0, est=4.256038255130912, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='223', iid='845', r_ui=4.0, est=3.2394660627083973, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='767', r_ui=1.0, est=1.347634240276493, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='640', iid='195', r_ui=4.0, est=4.78830498385087, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='288', iid='200', r_ui=4.0, est=4.113287043607598, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='494', iid='126', r_ui=4.0, est=4.049097725798686, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='148', iid='227', r_ui=4.0, est=3.4380541272290164, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='561', iid='642', r_ui=3.0, est=3.027629042128635, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='715', iid='202', r_ui=5.0, est=3.578223516079489, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='263', iid='174', r_ui=5.0, est=4.492189464194953, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='66', iid='741', r_ui=4.0, est=2.8700113530208116, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='416', iid='937', r_ui=2.0, est=3.904308176001535, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='389', iid='410', r_ui=3.0, est=3.3406594183896194, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='936', iid='257', r_ui=3.0, est=3.848594067497667, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='173', r_ui=5.0, est=2.927218272789678, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='409', iid='289', r_ui=1.0, est=2.6919373965797937, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='183', iid='222', r_ui=4.0, est=3.5522470607703607, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='26', iid='150', r_ui=3.0, est=3.446886851697821, details={'actual_k': 44, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='478', r_ui=5.0, est=4.61952453954573, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='72', iid='182', r_ui=5.0, est=4.106359472765427, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='222', iid='451', r_ui=3.0, est=3.2365589191497253, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='419', iid='1', r_ui=4.0, est=4.261832569461749, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='932', iid='490', r_ui=4.0, est=4.136976216399609, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='407', iid='244', r_ui=3.0, est=3.36543539222638, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='484', iid='22', r_ui=5.0, est=4.717806275029745, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='828', iid='331', r_ui=4.0, est=2.9276353215029967, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='250', iid='240', r_ui=4.0, est=2.9253224169664622, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='883', iid='286', r_ui=3.0, est=3.620219124431815, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='279', iid='63', r_ui=3.0, est=2.7239117380807563, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='313', iid='31', r_ui=4.0, est=3.6736478671746156, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='318', iid='238', r_ui=3.0, est=3.790629126614807, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='348', iid='245', r_ui=4.0, est=3.844875155123781, details={'actual_k': 26, 'was_impossible': False}),\n",
       " Prediction(uid='659', iid='13', r_ui=4.0, est=3.5465357618002655, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='343', iid='50', r_ui=5.0, est=4.790719838911102, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='602', iid='237', r_ui=4.0, est=4.4826646471926255, details={'actual_k': 15, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='8', r_ui=3.0, est=3.8339194189157055, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='614', iid='293', r_ui=3.0, est=3.9312879308395785, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='804', iid='152', r_ui=4.0, est=3.6663216922134576, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='239', iid='198', r_ui=5.0, est=4.422400691705155, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='655', iid='292', r_ui=2.0, est=3.1033467088223707, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='788', iid='301', r_ui=2.0, est=3.2585904446666367, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='588', iid='15', r_ui=5.0, est=4.200406882041795, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='787', iid='292', r_ui=3.0, est=3.6747886606786717, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='756', iid='402', r_ui=4.0, est=3.0753485260160183, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='385', iid='129', r_ui=3.0, est=3.3003284519976313, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='401', iid='751', r_ui=1.0, est=2.7886925726935914, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='435', iid='411', r_ui=3.0, est=2.8298611243565204, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='178', iid='508', r_ui=3.0, est=3.444029007559269, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='216', iid='433', r_ui=3.0, est=4.014103143326338, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='474', iid='608', r_ui=4.0, est=4.473272337005181, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='579', iid='238', r_ui=3.0, est=3.535417374492278, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='585', iid='283', r_ui=4.0, est=3.7140239600976646, details={'actual_k': 34, 'was_impossible': False}),\n",
       " Prediction(uid='505', iid='117', r_ui=4.0, est=3.6005666063164425, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='848', iid='504', r_ui=3.0, est=4.009478420367824, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='60', iid='95', r_ui=4.0, est=3.9247096755837894, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='676', iid='890', r_ui=1.0, est=2.132736715530456, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='109', iid='202', r_ui=5.0, est=4.260929602805084, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='586', iid='172', r_ui=4.0, est=3.890784379279836, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='264', r_ui=2.0, est=2.3207482486188713, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='7', iid='449', r_ui=3.0, est=3.4547721603620127, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='253', iid='655', r_ui=4.0, est=4.056157546332054, details={'actual_k': 41, 'was_impossible': False}),\n",
       " Prediction(uid='273', iid='319', r_ui=4.0, est=3.2514073382641655, details={'actual_k': 9, 'was_impossible': False}),\n",
       " Prediction(uid='197', iid='538', r_ui=3.0, est=3.3045656422657856, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='4', iid='354', r_ui=5.0, est=4.112838722670019, details={'actual_k': 8, 'was_impossible': False}),\n",
       " Prediction(uid='94', iid='786', r_ui=3.0, est=2.9857379075097317, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='717', iid='825', r_ui=2.0, est=3.376813078361265, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='373', iid='1147', r_ui=4.0, est=3.9506294384975145, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='773', iid='364', r_ui=4.0, est=2.052532162207352, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='62', iid='68', r_ui=1.0, est=3.231272837228643, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='698', iid='751', r_ui=3.0, est=2.436679010219776, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='559', iid='174', r_ui=4.0, est=3.7457913724242817, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='399', iid='470', r_ui=4.0, est=3.0630160118964236, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='380', iid='419', r_ui=3.0, est=3.159231079196431, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='897', iid='186', r_ui=5.0, est=4.132639696668519, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='811', iid='678', r_ui=5.0, est=4.0351903910962355, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='496', iid='485', r_ui=3.0, est=2.708023844673632, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='936', iid='1241', r_ui=4.0, est=3.00498873635241, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='749', iid='230', r_ui=3.0, est=3.6744393753323594, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='358', iid='318', r_ui=5.0, est=4.112563656374504, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='394', iid='117', r_ui=5.0, est=4.140599612530301, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='382', iid='122', r_ui=3.0, est=2.163327012967323, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='868', iid='631', r_ui=4.0, est=2.984401690067096, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='13', iid='896', r_ui=5.0, est=3.7335867686264073, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='867', iid='216', r_ui=3.0, est=4.144266758377529, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='712', iid='510', r_ui=2.0, est=3.8275656918163583, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='250', r_ui=4.0, est=3.739090784332254, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='694', iid='434', r_ui=5.0, est=4.291538621469082, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='466', iid='89', r_ui=3.0, est=3.9577548049089977, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='296', iid='251', r_ui=5.0, est=4.603081295129458, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='552', iid='977', r_ui=3.0, est=2.603353017795984, details={'actual_k': 41, 'was_impossible': False}),\n",
       " Prediction(uid='428', iid='750', r_ui=5.0, est=4.5656249367852855, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='397', iid='878', r_ui=1.0, est=2.163350334083722, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='279', iid='624', r_ui=4.0, est=3.1094186970521394, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='13', iid='908', r_ui=1.0, est=2.0090265263797886, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='653', iid='702', r_ui=3.0, est=2.341752789596764, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='335', iid='245', r_ui=4.0, est=3.8799877245789993, details={'actual_k': 6, 'was_impossible': False}),\n",
       " Prediction(uid='113', iid='508', r_ui=4.0, est=3.453838701297025, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='493', iid='124', r_ui=3.0, est=4.0739497395722655, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='100', iid='346', r_ui=3.0, est=3.4514038742381303, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='189', iid='501', r_ui=4.0, est=3.9010735046579894, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='297', iid='238', r_ui=5.0, est=3.7991402895871214, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='521', iid='248', r_ui=3.0, est=3.467939556745206, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='381', iid='95', r_ui=4.0, est=3.788722654112382, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='889', iid='357', r_ui=4.0, est=4.223358665738883, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='17', iid='151', r_ui=4.0, est=3.2503650700393782, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='300', r_ui=5.0, est=4.104538221932047, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='385', iid='408', r_ui=5.0, est=4.19058094360467, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='216', iid='249', r_ui=3.0, est=3.4538521342493014, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='440', iid='988', r_ui=1.0, est=2.338933370810262, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='437', iid='99', r_ui=4.0, est=3.7339003094516743, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='727', iid='80', r_ui=4.0, est=2.3767071794668015, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='324', iid='123', r_ui=4.0, est=4.159246153060934, details={'actual_k': 31, 'was_impossible': False}),\n",
       " Prediction(uid='299', iid='998', r_ui=2.0, est=2.411068063319611, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='245', iid='597', r_ui=4.0, est=3.4202437436039292, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='249', iid='56', r_ui=5.0, est=4.780458028503563, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='194', iid='203', r_ui=3.0, est=3.412184312984087, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='236', iid='98', r_ui=5.0, est=3.86062477810977, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='328', iid='322', r_ui=3.0, est=3.260601566742913, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='660', iid='657', r_ui=2.0, est=3.3561795504716634, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='495', iid='357', r_ui=5.0, est=4.789730832106714, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='148', iid='89', r_ui=5.0, est=4.51847427429783, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='774', iid='72', r_ui=1.0, est=1.7414668158452058, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='145', iid='55', r_ui=3.0, est=4.2254749182082465, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='372', iid='262', r_ui=4.0, est=4.362358332292665, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='14', iid='922', r_ui=4.0, est=4.364819952506425, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='1354', r_ui=1.0, est=1, details={'actual_k': 0, 'was_impossible': False}),\n",
       " Prediction(uid='648', iid='685', r_ui=5.0, est=3.3374503072143433, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='548', iid='683', r_ui=4.0, est=2.7847384764213436, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='798', iid='728', r_ui=4.0, est=3.1058774254895165, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='280', iid='1473', r_ui=3.0, est=3.806068849773926, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='706', iid='24', r_ui=3.0, est=3.547465930569624, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='504', iid='505', r_ui=4.0, est=4.020625017267665, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='488', iid='286', r_ui=1.0, est=3.219810303854944, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='258', iid='748', r_ui=5.0, est=3.7452580504877844, details={'actual_k': 18, 'was_impossible': False}),\n",
       " Prediction(uid='880', iid='554', r_ui=3.0, est=2.994115184745065, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='896', iid='461', r_ui=3.0, est=3.4685431109440845, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='362', iid='313', r_ui=4.0, est=4.628002612939258, details={'actual_k': 14, 'was_impossible': False}),\n",
       " Prediction(uid='533', iid='265', r_ui=3.0, est=3.9088119048909378, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='621', iid='404', r_ui=3.0, est=4.00765038418435, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='2', iid='277', r_ui=4.0, est=3.878851671258976, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='12', iid='684', r_ui=5.0, est=4.607771280279324, details={'actual_k': 25, 'was_impossible': False}),\n",
       " Prediction(uid='378', iid='1267', r_ui=3.0, est=3.0376712457421364, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='506', iid='425', r_ui=4.0, est=3.332215731071551, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='305', iid='210', r_ui=3.0, est=3.1724945697878897, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='357', iid='24', r_ui=4.0, est=4.57141295824014, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='303', iid='416', r_ui=3.0, est=3.9730240778741472, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='147', r_ui=4.0, est=3.7216948612364287, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='699', iid='748', r_ui=2.0, est=2.961928565873444, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='17', r_ui=4.0, est=3.23976790671963, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='899', iid='181', r_ui=3.0, est=3.9517087322760327, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='745', iid='188', r_ui=3.0, est=2.6561023012528704, details={'actual_k': 21, 'was_impossible': False}),\n",
       " Prediction(uid='567', iid='511', r_ui=2.0, est=4.1544928778645005, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='97', iid='435', r_ui=4.0, est=3.90904539900377, details={'actual_k': 34, 'was_impossible': False}),\n",
       " Prediction(uid='181', iid='1093', r_ui=1.0, est=2.000639137353528, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='394', iid='216', r_ui=3.0, est=4.385296547923697, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='568', iid='615', r_ui=5.0, est=3.725738674725296, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='115', iid='696', r_ui=4.0, est=3.693757187890746, details={'actual_k': 32, 'was_impossible': False}),\n",
       " Prediction(uid='401', iid='404', r_ui=2.0, est=2.995869741399352, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='456', iid='414', r_ui=3.0, est=3.5225926804363934, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='49', iid='300', r_ui=1.0, est=2.3855319334408778, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='312', iid='513', r_ui=5.0, est=5, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='723', iid='168', r_ui=5.0, est=3.5167514582032195, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='628', iid='168', r_ui=4.0, est=3.5290381565421614, details={'actual_k': 6, 'was_impossible': False}),\n",
       " Prediction(uid='260', iid='350', r_ui=4.0, est=3.4288202503456975, details={'actual_k': 10, 'was_impossible': False}),\n",
       " Prediction(uid='294', iid='358', r_ui=2.0, est=3.130625942077549, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='709', iid='1218', r_ui=4.0, est=3.637843851408785, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='301', iid='721', r_ui=3.0, est=3.623889347653237, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='70', iid='472', r_ui=3.0, est=3.106199393303077, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='887', iid='24', r_ui=5.0, est=3.979598949847463, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='40', iid='270', r_ui=3.0, est=2.740809376005901, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='334', iid='52', r_ui=4.0, est=3.860667407968786, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='560', iid='1016', r_ui=3.0, est=3.1179327557056795, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='122', iid='70', r_ui=5.0, est=4.071466204510406, details={'actual_k': 30, 'was_impossible': False}),\n",
       " Prediction(uid='788', iid='492', r_ui=3.0, est=3.673068967569177, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='87', iid='154', r_ui=4.0, est=4.035781330848637, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='532', iid='241', r_ui=5.0, est=4.49759915465514, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='293', iid='503', r_ui=4.0, est=3.3701737394361997, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='561', iid='12', r_ui=5.0, est=3.797296947509163, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='525', iid='322', r_ui=2.0, est=2.8805312309458686, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='508', iid='218', r_ui=2.0, est=3.0586101543464483, details={'actual_k': 45, 'was_impossible': False}),\n",
       " Prediction(uid='314', iid='294', r_ui=5.0, est=3.9792881770323785, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='174', iid='1230', r_ui=1.0, est=2.02555779480654, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='892', iid='425', r_ui=5.0, est=3.901235076963171, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='405', iid='731', r_ui=3.0, est=2.3835543519009357, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='899', iid='218', r_ui=4.0, est=3.2283229520356214, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='363', iid='96', r_ui=5.0, est=3.260126098655372, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='216', iid='302', r_ui=5.0, est=4.242997579246655, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='848', iid='153', r_ui=5.0, est=4.284871750121536, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='291', iid='95', r_ui=4.0, est=4.248877013165325, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='7', iid='501', r_ui=5.0, est=3.9562464379100364, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='58', iid='257', r_ui=5.0, est=3.605306700750862, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='13', iid='881', r_ui=2.0, est=2.4742387696368846, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='864', iid='1140', r_ui=1.0, est=2.7463218406561043, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='280', iid='22', r_ui=5.0, est=3.833450258629775, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='932', iid='890', r_ui=1.0, est=2.053108312472203, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='660', iid='1065', r_ui=2.0, est=3.047696577555722, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='504', iid='563', r_ui=3.0, est=2.4507930654814416, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='761', iid='214', r_ui=1.0, est=3.1942573564963124, details={'actual_k': 28, 'was_impossible': False}),\n",
       " Prediction(uid='243', iid='387', r_ui=4.0, est=3.5225742029773857, details={'actual_k': 40, 'was_impossible': False}),\n",
       " Prediction(uid='426', iid='332', r_ui=4.0, est=2.860881199207496, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='795', iid='50', r_ui=3.0, est=3.9629038294732677, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='894', iid='223', r_ui=4.0, est=4.271899898546376, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='151', iid='507', r_ui=5.0, est=4.173690806284257, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='804', iid='396', r_ui=3.0, est=2.770708043800234, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='94', iid='172', r_ui=4.0, est=4.3022947485832495, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='913', iid='183', r_ui=4.0, est=3.8483755440473817, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='331', iid='182', r_ui=4.0, est=3.554241012748034, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='72', iid='582', r_ui=4.0, est=3.852316873798434, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='749', iid='357', r_ui=4.0, est=4.273063020371949, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='437', iid='318', r_ui=4.0, est=4.346188351798849, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='96', iid='318', r_ui=5.0, est=4.8069917758560194, details={'actual_k': 29, 'was_impossible': False}),\n",
       " Prediction(uid='76', iid='333', r_ui=3.0, est=3.0999444845695665, details={'actual_k': 37, 'was_impossible': False}),\n",
       " Prediction(uid='684', iid='173', r_ui=3.0, est=4.2265505913148385, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='775', iid='313', r_ui=4.0, est=4.464104746970496, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='648', iid='208', r_ui=5.0, est=4.014044901011599, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='323', iid='199', r_ui=4.0, est=4.182368823919941, details={'actual_k': 39, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='1211', r_ui=3.0, est=3.8952517778246873, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='602', r_ui=4.0, est=3.9891945542968945, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='373', iid='660', r_ui=4.0, est=4.030425956707223, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='702', iid='687', r_ui=1.0, est=1, details={'actual_k': 11, 'was_impossible': False}),\n",
       " Prediction(uid='709', iid='217', r_ui=5.0, est=3.2285045240034393, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='450', iid='69', r_ui=4.0, est=4.257321757917208, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='401', iid='535', r_ui=2.0, est=2.6184657628581185, details={'actual_k': 40, 'was_impossible': False}),\n",
       " Prediction(uid='15', iid='286', r_ui=2.0, est=3.3371139743485627, details={'actual_k': 44, 'was_impossible': False}),\n",
       " Prediction(uid='417', iid='451', r_ui=4.0, est=3.33900327126822, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='438', iid='845', r_ui=4.0, est=3.865406520657564, details={'actual_k': 16, 'was_impossible': False}),\n",
       " Prediction(uid='755', iid='538', r_ui=4.0, est=3.2042892648446775, details={'actual_k': 13, 'was_impossible': False}),\n",
       " Prediction(uid='892', iid='100', r_ui=5.0, est=4.576879752252738, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='177', iid='651', r_ui=3.0, est=4.099194939388998, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='144', iid='173', r_ui=5.0, est=4.190197280156066, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='125', iid='69', r_ui=4.0, est=4.4030936364585, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='303', iid='844', r_ui=3.0, est=3.7713371784770713, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='913', iid='742', r_ui=3.0, est=2.970726279852938, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='753', iid='182', r_ui=3.0, est=3.13756089631251, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='201', iid='1131', r_ui=5.0, est=3.459772347898267, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='342', iid='3', r_ui=2.0, est=2.7548306451452507, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='764', iid='693', r_ui=3.0, est=3.591289322048112, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='749', iid='378', r_ui=5.0, est=4.067572332042394, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='756', iid='527', r_ui=3.0, est=3.5403715462609524, details={'actual_k': 42, 'was_impossible': False}),\n",
       " Prediction(uid='642', iid='216', r_ui=3.0, est=4.513379756052898, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='503', iid='740', r_ui=5.0, est=4.120686804867937, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='7', iid='577', r_ui=2.0, est=2.6628887308489677, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='60', iid='228', r_ui=4.0, est=4.0476868227725165, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='789', iid='286', r_ui=1.0, est=3.6443013630455376, details={'actual_k': 17, 'was_impossible': False}),\n",
       " Prediction(uid='651', iid='127', r_ui=4.0, est=4.425611715835292, details={'actual_k': 6, 'was_impossible': False}),\n",
       " Prediction(uid='6', iid='475', r_ui=5.0, est=3.561741600276753, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='262', iid='567', r_ui=1.0, est=2.586711833971541, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='903', iid='98', r_ui=5.0, est=4.677048787258271, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='95', iid='815', r_ui=3.0, est=3.332085769182185, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='79', r_ui=5.0, est=4.442531595999118, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='92', iid='144', r_ui=4.0, est=3.8759896007213643, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='416', iid='985', r_ui=3.0, est=3.242645502689288, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='262', iid='255', r_ui=3.0, est=3.0502167718074844, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='377', iid='316', r_ui=4.0, est=4.385411023679532, details={'actual_k': 12, 'was_impossible': False}),\n",
       " Prediction(uid='932', iid='459', r_ui=4.0, est=3.631358971347976, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='642', iid='117', r_ui=4.0, est=4.331550527927953, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='308', iid='425', r_ui=4.0, est=3.9556111018269196, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='336', iid='1183', r_ui=1.0, est=1.901783493569725, details={'actual_k': 49, 'was_impossible': False}),\n",
       " Prediction(uid='553', iid='190', r_ui=5.0, est=4.433572917815137, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='43', iid='1035', r_ui=4.0, est=3.317840912577107, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='88', r_ui=4.0, est=4.013616470246288, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='870', iid='169', r_ui=4.0, est=4.360744826503863, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='524', iid='175', r_ui=3.0, est=3.943764410665764, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='144', iid='195', r_ui=5.0, est=3.9656480441161768, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='455', iid='170', r_ui=3.0, est=4.0698911701022915, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='741', iid='367', r_ui=2.0, est=3.339398422542366, details={'actual_k': 35, 'was_impossible': False}),\n",
       " Prediction(uid='203', iid='477', r_ui=4.0, est=2.9180314376864582, details={'actual_k': 20, 'was_impossible': False}),\n",
       " Prediction(uid='664', iid='531', r_ui=2.0, est=3.8757779625964677, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='514', iid='483', r_ui=4.0, est=4.4174626492770335, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='125', iid='997', r_ui=2.0, est=2.3001583216586896, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='627', iid='11', r_ui=4.0, est=3.6501461748816615, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='22', iid='290', r_ui=5.0, est=3.260912656593615, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='711', iid='58', r_ui=4.0, est=4.033833581619562, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='294', iid='475', r_ui=5.0, est=4.2468833768495236, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='276', iid='1042', r_ui=1.0, est=3.2728396852016313, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='100', iid='344', r_ui=4.0, est=3.57631626341136, details={'actual_k': 19, 'was_impossible': False}),\n",
       " Prediction(uid='919', iid='244', r_ui=2.0, est=3.3975796576772583, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='534', iid='628', r_ui=5.0, est=4.41988514996649, details={'actual_k': 40, 'was_impossible': False}),\n",
       " Prediction(uid='399', iid='597', r_ui=3.0, est=2.596267090903231, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='935', iid='300', r_ui=4.0, est=4.381774070294673, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='788', iid='436', r_ui=3.0, est=3.376782942412347, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='689', iid='405', r_ui=5.0, est=3.9581575988683584, details={'actual_k': 23, 'was_impossible': False}),\n",
       " Prediction(uid='901', iid='321', r_ui=1.0, est=3.2292377333785867, details={'actual_k': 38, 'was_impossible': False}),\n",
       " Prediction(uid='790', iid='748', r_ui=1.0, est=2.9483544148263277, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='366', iid='219', r_ui=5.0, est=3.7103648198071797, details={'actual_k': 22, 'was_impossible': False}),\n",
       " Prediction(uid='645', iid='286', r_ui=4.0, est=3.9957380869913726, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='938', iid='1016', r_ui=3.0, est=3.4260737172656035, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='313', iid='172', r_ui=4.0, est=4.0433439684520485, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='922', iid='391', r_ui=3.0, est=2.925681295684968, details={'actual_k': 48, 'was_impossible': False}),\n",
       " Prediction(uid='429', iid='92', r_ui=4.0, est=3.685972374082866, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='3', iid='327', r_ui=4.0, est=3.0062513444538865, details={'actual_k': 33, 'was_impossible': False}),\n",
       " Prediction(uid='487', iid='276', r_ui=3.0, est=3.8428734358115597, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='710', iid='327', r_ui=3.0, est=3.2855839276047183, details={'actual_k': 43, 'was_impossible': False}),\n",
       " Prediction(uid='226', iid='169', r_ui=5.0, est=4.630725391432758, details={'actual_k': 24, 'was_impossible': False}),\n",
       " Prediction(uid='833', iid='483', r_ui=4.0, est=4.194076856537617, details={'actual_k': 50, 'was_impossible': False}),\n",
       " Prediction(uid='483', iid='151', r_ui=2.0, est=3.074426635114383, details={'actual_k': 24, 'was_impossible': False}),\n",
       " ...]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item-based Model : Test Set\n",
      "RMSE: 0.9129\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9128564680469767"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get RMSE\n",
    "print(\"Item-based Model : Test Set\")\n",
    "accuracy.rmse(test_pred, verbose=True)"
   ]
  }
 ],
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   "display_name": "Python 3",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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