Variational Inference for Sparse and Undirected Models
This work addresses a bottleneck in applying Bayesian methods to domains like genomics and neuroscience, offering a scalable solution for sparse interaction modeling.
The authors tackled the problem of Bayesian inference for sparse undirected graphical models, which is hindered by doubly intractable Monte Carlo sampling, by developing Persistent VI and Fadeout methods, resulting in substantial improvements in learning sparse models in simulated and real-world physics and biology problems.
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.