Efficient Gradient-Based Inference through Transformations between Bayes Nets and Neural Nets

TL;DR

This paper demonstrates how hierarchical Bayesian networks and neural networks can be transformed into each other through parameterization choices, improving the efficiency and robustness of gradient-based inference.

Contribution

It introduces a method to switch between centered and non-centered parameterizations, enhancing inference efficiency and robustness in Bayesian and neural network models.

Findings

Transformations enable switching between Bayesian and neural network models.

Non-centered parameterization allows simple Monte Carlo estimation of marginal likelihood.

Theoretical insights are validated through experiments.

Abstract

Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by switching between centered and differentiable non-centered parameterizations of the latent variables. The choice of parameterization greatly influences the efficiency of gradient-based posterior inference; we show that they are often complementary to eachother, we clarify when each parameterization is preferred and show how inference can be made robust. In the non-centered form, a simple Monte Carlo estimator of the marginal likelihood can be used for learning the parameters. Theoretical results are supported by experiments.