-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathblack_box_alphavi.py
178 lines (139 loc) · 6.59 KB
/
black_box_alphavi.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
from __future__ import absolute_import
from __future__ import print_function
import autograd.numpy as np
import autograd.numpy.random as npr
import autograd.scipy.stats.norm as norm
from autograd.scipy.special import logsumexp
from autograd import grad
from autograd.util import quick_grad_check
import pandas as pd
import sys
import math
class WeightsParser(object):
"""A helper class to index into a parameter vector."""
def __init__(self):
self.idxs_and_shapes = {}
self.num_weights = 0
def add_shape(self, name, shape):
start = self.num_weights
self.num_weights += np.prod(shape)
self.idxs_and_shapes[ name ] = (slice(start, self.num_weights), shape)
def get(self, vect, name):
idxs, shape = self.idxs_and_shapes[name]
return np.reshape(vect[ idxs ], shape)
def get_indexes(self, vect, name):
idxs, shape = self.idxs_and_shapes[name]
return idxs
def make_functions(d, shapes, alpha):
N = sum((m + 1) * n for m, n in shapes)
parser = WeightsParser()
parser.add_shape('mean', (N, 1))
parser.add_shape('log_variance', (N, 1))
parser.add_shape('log_v_noise', (1, 1))
w = 0.1 * np.random.randn(parser.num_weights)
w[ parser.get_indexes(w, 'log_variance') ] = w[ parser.get_indexes(w, 'log_variance') ] - 10.0
w[ parser.get_indexes(w, 'log_v_noise') ] = np.log(1.0)
def predict(samples_q, X):
# First layer
K = samples_q.shape[ 0 ]
(m, n) = shapes[ 0 ]
W = samples_q[ : , : m * n ].reshape((n * K, m)).T
b = samples_q[ : , m * n : m * n + n ].reshape(1, n * K)
a = np.dot(X, W) + b
h = np.maximum(a, 0)
# Second layer
samples_q = samples_q[ : , m * n + n : ]
(m, n) = shapes[ 1 ]
b = samples_q[ : , m * n : m * n + n ].T
a = np.sum((samples_q[ : , : m * n ].reshape(1, -1) * h).reshape((K * X.shape[ 0 ], m)),
1).reshape((X.shape[ 0 ], K)) + b
return a
def log_likelihood_factor(samples_q, v_noise, X, y):
outputs = predict(samples_q, X)
log_p = -0.5 * np.log(2 * math.pi * v_noise) - 0.5 * (np.tile(y, (1, samples_q.shape[ 0 ])) - outputs)**2 / v_noise
return np.mean(log_p, 0)
def log_q(samples_q, q):
log_q = -0.5 * np.log(2 * math.pi * q[ 'v' ]) - 0.5 * (samples_q - q[ 'm' ]) **2 / q[ 'v' ]
return np.sum(log_q, 1)
def log_prior(samples_q, v_prior):
log_p0 = -0.5 * np.log(2 * math.pi * v_prior) - 0.5 * samples_q **2 / v_prior
return np.sum(log_p0, 1)
def draw_samples(q, K):
return npr.randn(K, len(q[ 'm' ])) * np.sqrt(q[ 'v' ]) + q[ 'm' ]
def get_parameters_q(w, v_prior, scale = 1.0):
v = 1.0 / (scale * np.exp(-parser.get(w, 'log_variance'))[ :, 0 ] + 1.0 / v_prior)
m = scale * parser.get(w, 'mean')[ :, 0 ] * np.exp(-parser.get(w, 'log_variance')[ :, 0 ]) * v
return { 'm': m, 'v': v }
def energy(w, X, y, v_prior, K, N, is_max = "no"):
q = get_parameters_q(w, v_prior)
v_noise = np.exp(parser.get(w, 'log_v_noise')[ 0, 0 ])
samples_q = draw_samples(q, K)
log_factor_value = 1.0 * N * log_likelihood_factor(samples_q, v_noise, X, y)
if is_max == "yes":
logp0 = log_prior(samples_q, v_prior)
logq = log_q(samples_q, q)
logF = logp0 + log_factor_value - logq
vfe = -np.max(logF)
elif alpha > 1.0 - 10e-5 and alpha < 1.0 + 10e-5:
KL = np.sum(-0.5 * np.log(2 * math.pi * v_prior) - 0.5 * (q[ 'm' ]**2 + q[ 'v' ]) / v_prior) - \
np.sum(-0.5 * np.log(2 * math.pi * q[ 'v' ] * np.exp(1)))
vfe = -(np.mean(log_factor_value) + KL)
else:
logp0 = log_prior(samples_q, v_prior)
logq = log_q(samples_q, q)
logF = logp0 + log_factor_value - logq
logF = (1 - alpha) * logF
vfe = -(logsumexp(logF) - np.log(K))
vfe = vfe / (1 - alpha)
return vfe
def get_error_and_ll(w, v_prior, X, y, K, location, scale):
v_noise = np.exp(parser.get(w, 'log_v_noise')[ 0, 0 ]) * scale**2
q = get_parameters_q(w, v_prior)
samples_q = draw_samples(q, K)
outputs = predict(samples_q, X) * scale + location
log_factor = -0.5 * np.log(2 * math.pi * v_noise) - 0.5 * (np.tile(y, (1, K)) - np.array(outputs))**2 / v_noise
ll = np.mean(logsumexp(log_factor - np.log(K), 1))
error = np.sqrt(np.mean((y - np.mean(outputs, 1, keepdims = True))**2))
return error, ll
def update_v_prior(w, v_prior):
q = get_parameters_q(w, v_prior)
return np.mean(q[ 'm' ]**2 + q[ 'v' ])
return w, energy, update_v_prior, get_error_and_ll
def make_batches(N_data, batch_size):
return [ slice(i, min(i + batch_size, N_data)) for i in range(0, N_data, batch_size) ]
def fit_q(X, y, hidden_layer_size, batch_size, epochs, K, alpha = 1.0, learning_rate = 1e-2, v_prior = 1.0):
hidden_layer_size = [ hidden_layer_size ]
hidden_layer_size = np.array([ X.shape[ 1 ] ] + hidden_layer_size + [ 1 ])
shapes = list(zip(hidden_layer_size[ : -1 ], hidden_layer_size[ 1 : ]))
w, energy, update_v_prior, get_error_and_ll = make_functions(X.shape[ 1 ], shapes, alpha)
energy_grad = grad(energy)
# Check the gradients numerically, just to be safe
#quick_grad_check(energy, w, (X, y, v_prior, K, X.shape[ 0 ]))
#print(" Epoch | Error | Log-likelihood ")
def print_perf(epoch, w):
error, ll = get_error_and_ll(w, v_prior, X, y, K, 0.0, 1.0)
print("{0:15}|{1:15}|{2:15}".format(epoch, error, ll))
sys.stdout.flush()
# Train with sgd
batch_idxs = make_batches(X.shape[0], batch_size)
m1 = 0
m2 = 0
beta1 = 0.9
beta2 = 0.999
epsilon = 1e-8
t = 0
for epoch in range(epochs):
permutation = np.random.choice(range(X.shape[ 0 ]), X.shape[ 0 ], replace = False)
#print_perf(epoch, w)
for idxs in batch_idxs:
t += 1
if alpha > -10**5:
grad_w = energy_grad(w, X[ permutation[ idxs ] ], y[ permutation[ idxs ] ], v_prior, K, X.shape[ 0 ])
else:
grad_w = energy_grad(w, X[ permutation[ idxs ] ], y[ permutation[ idxs ] ], v_prior, K, X.shape[ 0 ], is_max = "yes")
m1 = beta1 * m1 + (1 - beta1) * grad_w
m2 = beta2 * m2 + (1 - beta2) * grad_w**2
m1_hat = m1 / (1 - beta1**t)
m2_hat = m2 / (1 - beta2**t)
w -= learning_rate * m1_hat / (np.sqrt(m2_hat) + epsilon)
return w, v_prior, get_error_and_ll