Forward Amortized Inference for Likelihood-Free Variational Marginalization

TL;DR

This paper introduces a likelihood-free, forward KL-based amortized variational inference method that efficiently marginalizes over latent variables and is proven to optimize the exact posterior marginals in a mean-field setting.

Contribution

It presents a novel forward KL divergence-based variational loss that is likelihood-free and allows for easy marginalization over latent variables, with theoretical guarantees.

Findings

Successfully trained a Bayesian forecaster for atmospheric convection.

Developed a meta-classification network solving arbitrary problems without additional training.

Proved the variational loss optimizes the exact posterior marginals.

Abstract

In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.