Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping

TL;DR

The paper introduces Half-VAE, a novel encoder-free variational autoencoder that directly optimizes latent variables for inverse problems like ICA, bypassing the need for explicit inverse mappings and the encoder.

Contribution

It proposes a new VAE architecture that eliminates the encoder, enabling direct optimization of latent variables for inverse problems such as ICA.

Findings

Half-VAE successfully solves ICA without an encoder.

Latent variables become mutually independent through training.

The approach simplifies inverse problem solving by removing the encoder component.

Abstract

Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a variety of problems, including those related to causal inference. Variational inference, a subset of Bayesian inference, is primarily used to efficiently approximate complex posterior distributions. Variational Autoencoders (VAEs), which combine variational inference with deep learning, have become widely applied across various domains. This study explores the potential of VAEs for solving inverse problems, such as Independent Component Analysis (ICA), without relying on an explicit inverse mapping process. Unlike other VAE-based ICA methods, this approach discards the encoder in the VAE architecture, directly setting the latent variables as trainable parameters. In other words, the latent variables are no longer outputs of the encoder but are instead optimized directly through the objective function to converge to appropriate values. We find that, with a suitable prior setup, the latent variables, represented by trainable parameters, can exhibit mutually independent properties as the parameters converge, all without the need for an encoding process. This approach, referred to as the Half-VAE, bypasses the inverse mapping process by eliminating the encoder. This study demonstrates the feasibility of using the Half-VAE to solve ICA without the need for an explicit inverse mapping process.