Exploring Exchangeable Dataset Amortization for Bayesian Posterior Inference

Bayesian inference provides a natural way of incorporating uncertainties and different underlying theories when making predictions or analyzing complex systems. However, it requires computationally expensive routines for approximation, which have to be re-run when new data is observed and are thus infeasible to efficiently scale and reuse. In this work, we look at the problem from the perspective of amortized inference to obtain posterior parameter distributions for known probabilistic models. We propose a neural network-based approach that can handle exchangeable observations and amortize over datasets to convert the problem of Bayesian posterior inference into a single forward pass of a network. Our empirical analyses explore various design choices for amortized inference by comparing: (a) our proposed variational objective with forward KL minimization, (b) permutation-invariant architectures like Transformers and DeepSets, and (c) parameterizations of posterior families like diagonal Gaussian and Normalizing Flows. Through our experiments, we successfully apply amortization techniques to estimate the posterior distributions for different domains solely through inference.