Efficient Gradient-Based Inference through Transformations between Bayes Nets and Neural Nets
This work addresses a methodological bottleneck for researchers in probabilistic modeling and machine learning, offering incremental improvements in inference efficiency.
The paper tackles the challenge of efficient gradient-based posterior inference by transforming between hierarchical Bayesian networks and neural networks with stochastic hidden units, showing that the choice of parameterization (centered vs. non-centered) significantly affects efficiency and clarifying when each is preferred, with experimental support.
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.