Discovery of Single Independent Latent Variable

TL;DR

This paper introduces a novel autoencoder-based method with a discriminator to recover a hidden independent component from an invertible mixture, achieving identifiable results in specific ICA scenarios.

Contribution

It presents a new approach for latent variable discovery in invertible mixtures with one observed and one hidden component, improving identifiability in certain ICA cases.

Findings

Successfully recovers hidden components in various tasks

Achieves entropy-preserving recovery of the independent component

Demonstrates effectiveness in image, voice, and ECG applications

Abstract

Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science. In this work, we consider data given as an invertible mixture of two statistically independent components and assume that one of the components is observed while the other is hidden. Our goal is to recover the hidden component. For this purpose, we propose an autoencoder equipped with a discriminator. Unlike the standard nonlinear ICA problem, which was shown to be non-identifiable, in the special case of ICA we consider here, we show that our approach can recover the component of interest up to entropy-preserving transformation. We demonstrate the performance of the proposed approach in several tasks, including image synthesis, voice cloning, and fetal ECG extraction.