Half-AVAE: Adversarial-Enhanced Factorized and Structured Encoder-Free VAE for Underdetermined Independent Component Analysis

Abstract: This study advances the Variational Autoencoder (VAE) framework by addressing challenges in Independent Component Analysis (ICA) under both determined and underdetermined conditions, focusing on enhancing the independence and interpretability of latent variables. Traditional VAEs map observed data to latent variables and back via an encoder-decoder architecture, but struggle with underdetermined ICA where the number of latent variables exceeds observed signals. The proposed Half Adversarial VAE (Half-AVAE) builds on the encoder-free Half-VAE framework, eliminating explicit inverse mapping to tackle underdetermined scenarios. By integrating adversarial networks and External Enhancement (EE) terms, Half-AVAE promotes mutual independence among latent dimensions, achieving factorized and interpretable representations. Experiments with synthetic signals demonstrate that Half-AVAE outperforms baseline models, including GP-AVAE and Half-VAE, in recovering independent components under underdetermined conditions, as evidenced by lower root mean square errors. The study highlights the flexibility of VAEs in variational inference, showing that encoder omission, combined with adversarial training and structured priors, enables effective solutions for complex ICA tasks, advancing applications in disentanglement, causal inference, and generative modeling.