Independent component analysis is a core framework within blind source separation for recovering latent source signals from observed mixtures under statistical independence assumptions. In this work, we propose PDGMM-VAE, a source-oriented variational autoencoder in which each latent dimension, interpreted explicitly as an individual source component, is assigned its own adaptive Gaussian mixture model prior. The proposed framework imposes heterogeneous per-dimension prior constraints, enabling different latent dimensions to model different non-Gaussian source marginals within a unified probabilistic encoder-decoder architecture. The parameters of these source-specific GMM priors are not fixed in advance, but are jointly learned together with the encoder and decoder under the overall training objective. Beyond the model construction itself, we provide a theoretical analysis clarifying why adaptive per-dimension prior design is meaningful in this setting. In particular, we show that heterogeneous per-dimension priors reduce latent permutation symmetry relative to homogeneous shared priors, and we further show that the KL regularization induced by the adaptive GMM prior creates source-specific attraction behavior that helps explain source-wise specialization during training. We also clarify the relation of the proposed model to the standard VAE and provide a weak recovery statement in an idealized linear low-noise regime. Experimental results on both linear and nonlinear mixing problems show that PDGMM-VAE can recover latent source signals and fit source-specific non-Gaussian marginals effectively. These results suggest that adaptive per-dimension mixture-prior design provides a principled and promising direction for VAE-based ICA and source-oriented generative modeling.
Figures & tables
Figure 1: Illustration of the proposed PDGMM-VAE framework. Each latent dimension is regularized by an adaptive Gaussian mixture prior whose parameters are jointly learned during training.
Figure 2: Training curves in the linear ICA experiment, including the total loss, posterior variances, GMM means, GMM variances, GMM weights, and per-source maximum correlations.
Figure 3: Comparison between the true sources and the inferred posterior means in the linear ICA experiment after z-score normalization. The shaded regions denote the posterior uncertainty bands.
Figure 4: True and estimated source distributions for Source 1 in the linear ICA experiment.
Figure 5: True and estimated source distributions for Source 2 in the linear ICA experiment.
Figure 6: True and estimated source distributions for Source 3 in the linear ICA experiment.
Figure 7: Training curves in the nonlinear ICA experiment, including the total loss, posterior variances, GMM means, GMM variances, GMM weights, and per-source maximum correlations.
Figure 8: Comparison between the true sources and the inferred posterior means in the nonlinear ICA experiment after z-score normalization. The shaded regions denote the posterior uncertainty bands.
Figure 9: True and estimated source distributions for Source 1 in the nonlinear ICA experiment.
Figure 10: True and estimated source distributions for Source 2 in the nonlinear ICA experiment.
Figure 11: True and estimated source distributions for Source 3 in the nonlinear ICA experiment.