Implicit Variational Inference for High-Dimensional Posteriors

TL;DR

This paper introduces a novel neural sampler-based implicit variational inference method capable of approximating complex, high-dimensional posteriors, including in large Bayesian neural networks, outperforming existing uncertainty quantification techniques.

Contribution

The paper presents a new implicit variational inference approach with a scalable neural sampler architecture and novel bounds, enabling effective approximation of large, multimodal posteriors without adversarial training.

Findings

Successfully recover correlations in large Bayesian neural networks

Outperform state-of-the-art uncertainty quantification methods

Enable implicit distributions over tens of millions of variables

Abstract

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.