Variational Inference for Sparse and Undirected Models

TL;DR

This paper introduces scalable Bayesian inference methods for sparse undirected graphical models, overcoming computational challenges with novel variational algorithms that improve learning in biological and physical data.

Contribution

It presents Persistent VI and Fadeout, two new variational inference techniques that enable efficient Bayesian analysis of discrete undirected models with sparsity.

Findings

Improved inference accuracy in simulated data.

Enhanced learning performance in biological datasets.

Reduced computational complexity compared to traditional methods.

Abstract

Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts, they are rarely used because they require doubly intractable Monte Carlo sampling. Here, we develop a framework for scalable Bayesian inference of discrete undirected models based on two new methods. The first is Persistent VI, an algorithm for variational inference of discrete undirected models that avoids doubly intractable MCMC and approximations of the partition function. The second is Fadeout, a reparameterization approach for variational inference under sparsity-inducing priors that captures a posteriori correlations between parameters and hyperparameters with noncentered parameterizations. We find that, together, these methods for variational inference substantially improve learning of sparse undirected graphical models in simulated and real problems from physics and biology.