Recursive Inference for Variational Autoencoders

TL;DR

This paper introduces a recursive mixture estimation algorithm for VAEs that enhances posterior approximation accuracy while maintaining fast inference, outperforming existing semi-amortized methods.

Contribution

The paper proposes a novel recursive mixture inference algorithm for VAEs that improves posterior approximation and inference speed compared to prior semi-amortized approaches.

Findings

Higher test data likelihood on benchmark datasets

Faster inference requiring only a single feed-forward pass

Outperforms state-of-the-art methods in accuracy

Abstract

Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposed to address this drawback; however, their iterative gradient update procedures can be computationally demanding. To address these issues, in this paper we introduce an accurate amortized inference algorithm. We propose a novel recursive mixture estimation algorithm for VAEs that iteratively augments the current mixture with new components so as to maximally reduce the divergence between the variational and the true posteriors. Using the functional gradient approach, we devise an intuitive learning criteria for selecting a new mixture component: the new component has to improve the data likelihood (lower bound) and, at the same time, be as divergent from the current mixture distribution as possible, thus increasing representational diversity. Compared to recently proposed boosted variational inference (BVI), our method relies on amortized inference in contrast to BVI's non-amortized single optimization instance. A crucial benefit of our approach is that the inference at test time requires a single feed-forward pass through the mixture inference network, making it significantly faster than the semi-amortized approaches. We show that our approach yields higher test data likelihood than the state-of-the-art on several benchmark datasets.