Benchmark potentials in PyTorch

This package provides potential functions to benchmark sampling and optimization algorithms.

Synthetic potentials include:

• Standard Gaussian
• Diagonal Gaussian (several variants)
• Block diagonal Gaussian (several variants)
• Full rank Gaussian (several variants)
• Multimodal (several variants)
• Funnel
• Rosenbrock

Real-world potentials include various model posteriors:

• Eight schools
• German credit
• Sparse German credit
• Radon (varying intercepts)
• Radon (varying slopes)
• Radon (varying intercepts and slopes)
• Synthetic item response theory
• Stochastic volatility model

Image-based potentials include $\phi^4$ lattice field theory targets with varying lattice sizes.

Usage instructions

The main components in the package are callable Potential objects. They can be used to compute the negative unnormalized log probability density. In most synthetic examples, Potential objects also provide a sample function which lets us draw true samples from their underlying distributions. We provide an example for the funnel potential:

import torch
from potentials.synthetic.funnel import Funnel

torch.manual_seed(0)

# Create the potential object
potential = Funnel()

batch_shape = (50,)

# Randomly generate some input data
x = torch.randn(size=(*batch_shape, *potential.event_shape)) / 10

# Compute the potential value at input points
value = potential(x)  # value.shape == (50,)

# Draw 50 samples from the underlying distribution
x_new = potential.sample(batch_shape)  # x_new.shape == (50, 100)

Installing

This package requires Python version 3.7 or greater.

Install the package directly from Github:

pip install git+https://github.com/davidnabergoj/potentials.git

To alternatively configure the package for local development, clone the repository and install dependencies as follows:

git clone [email protected]:davidnabergoj/potentials.git
pip install -r requirements.txt

Citation

If you use this code in your work, kindly consider citing the accompanying paper:

Nabergoj and Štrumbelj: Empirical evaluation of normalizing flows in Markov Chain Monte Carlo, 2024. arxiv:2412.17136.

BibTex entry:

@misc{nabergoj_nf_mcmc_evaluation_2024,
    author = {Nabergoj, David and \v{S}trumbelj, Erik},
    title = {Empirical evaluation of normalizing flows in {Markov} {Chain} {Monte} {Carlo}},
    publisher = {arXiv},
    month = dec,
    year = {2024},
    note = {arxiv:2412.17136}
}