A Unified Latent Space Disentanglement VAE Framework with Robust Disentanglement Effectiveness Evaluation

Evaluating and interpreting latent representations, such as variational autoencoders (VAEs), remains a significant challenge for diverse data types, especially when ground-truth generative factors are unknown. To address this, we propose a general framework -- bfVAE -- that unifies several state-of-the-art disentangled VAE approaches and generates effective latent space disentanglement, especially for tabular data. To assess the effectiveness of a VAE disentanglement technique, we propose two procedures - Feature Variance Heterogeneity via Latent Traversal (FVH-LT) and Dirty Block Sparse Regression in Latent Space (DBSR-LS) for disentanglement assessment, along with the latent space disentanglement index (LSDI) which uses the outputs of FVH-LT and DBSR-LS to summarize the overall effectiveness of a VAE disentanglement method without requiring access to or knowledge of the ground-truth generative factors. To the best of our knowledge, these are the first assessment tools to achieve this. FVH-LT and DBSR-LS also enhance latent space interpretability and provide guidance on more efficient content generation. To ensure robust and consistent disentanglement, we develop a greedy alignment strategy (GAS) that mitigates label switching and aligns latent dimensions across runs to obtain aggregated results. We assess the bfVAE framework and validate FVH-LT, DBSR-LS, and LSDI in extensive experiments on tabular and image data. The results suggest that bfVAE surpasses existing disentangled VAE frameworks in terms of disentanglement quality, robustness, achieving a near-zero false discovery rate for informative latent dimensions, that FVH-LT and DBSR-LS reliably uncover semantically meaningful and domain-relevant latent structures, and that LSDI makes an effective overall quantitative summary on disentanglement effectiveness.