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

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 pa-rameterizations of the latent variables. The choice of parameterization greatly influences the efficiency of gradient-based posterior in-ference; we show that they are often comple-mentary 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 estima-tor of the marginal likelihood can be used for learning the parameters. Theoretical results are supported by experiments. 1