Lin-Yong Cui

Yuan-Hao Wei, Fu-Hao Deng, Lin-Yong Cui et al.

Blind source separation (BSS) seeks to recover latent source signals from observed mixtures. Variational autoencoders (VAEs) offer a natural perspective for this problem: the latent variables can be interpreted as source components, the encoder can be viewed as a demixing mapping from observations to sources, and the decoder can be regarded as a remixing process from inferred sources back to observations. In this work, we propose AR-Flow VAE, a novel VAE-based framework for BSS in which each latent source is endowed with a parameter-adaptive autoregressive flow prior. This prior significantly enhances the flexibility of latent source modeling, enabling the framework to capture complex non-Gaussian behaviors and structured dependencies, such as temporal correlations, that are difficult to represent with conventional priors. In addition, the structured prior design assigns distinct priors to different latent dimensions, thereby encouraging the latent components to separate into different source signals under heterogeneous prior constraints. Experimental results validate the effectiveness of the proposed architecture for blind source separation. More importantly, this work provides a foundation for future investigations into the identifiability and interpretability of AR-Flow VAE.

Yuan-Hao Wei, Fu-Hao Deng, Lin-Yong Cui et al.

The interpretability of generative models is considered a key factor in demonstrating their effectiveness and controllability. The generated data are believed to be determined by latent variables that are not directly observable. Therefore, disentangling, decoupling, decomposing, causal inference, or performing Independent Component Analysis (ICA) in the latent variable space helps uncover the independent factors that influence the attributes or features affecting the generated outputs, thereby enhancing the interpretability of generative models. As a generative model, Variational Autoencoders (VAEs) combine with variational Bayesian inference algorithms. Using VAEs, the inverse process of ICA can be equivalently framed as a variational inference process. In some studies, Gaussian processes (GPs) have been introduced as priors for each dimension of latent variables in VAEs, structuring and separating each dimension from temporal or spatial perspectives, and encouraging different dimensions to control various attributes of the generated data. However, GPs impose a significant computational burden, resulting in substantial resource consumption when handling large datasets. Essentially, GPs model different temporal or spatial structures through various kernel functions. Structuring the priors of latent variables via kernel functions-so that different kernel functions model the correlations among sequence points within different latent dimensions-is at the core of achieving disentanglement in VAEs. The proposed Structured Kernel Regression VAE (SKR-VAE) leverages this core idea in a more efficient way, avoiding the costly kernel matrix inversion required in GPs. This research demonstrates that, while maintaining ICA performance, SKR-VAE achieves greater computational efficiency and significantly reduced computational burden compared to GP-VAE.