CASL-VAE: Learning Structured Latent Variables from Unpaired Data for Semi-supervised Clustering and Paired Sample Generation

CASL-VAE (Contrastive Analysis with Structured Latents via Variational Autoencoder) addresses the challenge of comparing two populations (e.g., healthy controls vs. patients) when paired data is unavailable. The authors propose a deep generative framework that uses variational inference to decompose data into two distinct latent components: a common latent space capturing shared variation (e.g., demographic or scanner effects) and a hierarchical salient latent space capturing target-specific heterogeneity. The salient latent is further structured into discrete categories to represent distinct subtypes and continuous variables to capture variation within those subtypes.

The model is trained on unpaired data by optimizing a joint variational lower bound. To ensure the latent spaces are correctly disentangled, the authors introduce several regularization terms:

• Maximum Mean Discrepancy (MMD) to align the common latent distributions across domains.
• Sample-level Latent Consistency to ensure that decoding a common latent with a neutral salient state produces a consistent reference-domain sample.
• Domain-level Supervision (using binary cross-entropy) to force reference samples into a specific category, leaving the remaining categories to capture target-specific heterogeneity.

This architecture allows the model to perform unsupervised subtype discovery and generate synthetic paired samples by manipulating the salient latent variables while keeping the common latent fixed.

In many scientific and clinical fields, such as neuroimaging or genomics, researchers often have access to large datasets of healthy and diseased individuals but lack paired observations for the same subjects. Standard generative models often entangle these sources of variation, making it difficult to isolate disease-specific patterns. CASL-VAE provides a principled, interpretable way to perform contrastive analysis, allowing researchers to identify biologically plausible disease subtypes and generate counterfactual samples (e.g., what a patient's brain might look like if they were healthy) without needing direct supervision.