Multimodal Variational Autoencoder: a Barycentric View

TL;DR

This paper introduces a barycentric framework for multimodal variational autoencoders, leveraging different divergence measures like Wasserstein distance to improve the learning of shared and modality-specific representations across multiple data modalities.

Contribution

It provides a novel theoretical formulation of multimodal VAEs using barycenters, extending existing methods with flexible divergence choices, notably the Wasserstein barycenter.

Findings

Wasserstein barycenter better preserves distribution geometry.

The proposed method outperforms traditional PoE and MoE approaches.

Empirical results on three benchmarks validate effectiveness.

Abstract

Multiple signal modalities, such as vision and sounds, are naturally present in real-world phenomena. Recently, there has been growing interest in learning generative models, in particular variational autoencoder (VAE), to for multimodal representation learning especially in the case of missing modalities. The primary goal of these models is to learn a modality-invariant and modality-specific representation that characterizes information across multiple modalities. Previous attempts at multimodal VAEs approach this mainly through the lens of experts, aggregating unimodal inference distributions with a product of experts (PoE), a mixture of experts (MoE), or a combination of both. In this paper, we provide an alternative generic and theoretical formulation of multimodal VAE through the lens of barycenter. We first show that PoE and MoE are specific instances of barycenters, derived by minimizing the asymmetric weighted KL divergence to unimodal inference distributions. Our novel formulation extends these two barycenters to a more flexible choice by considering different types of divergences. In particular, we explore the Wasserstein barycenter defined by the 2-Wasserstein distance, which better preserves the geometry of unimodal distributions by capturing both modality-specific and modality-invariant representations compared to KL divergence. Empirical studies on three multimodal benchmarks demonstrated the effectiveness of the proposed method.