Disentanglement Analysis in Deep Latent Variable Models Matching Aggregate Posterior Distributions

2025-01-26

AI Summary

This work addresses the limitation in disentanglement evaluation of deep latent variable models (DLVMs)—such as VAEs, AAEs, and WAE-MMDs—that relies excessively on the assumption that latent variables align with coordinate axes. We propose an unsupervised statistical evaluation framework grounded in aggregated posterior matching and statistical dependence analysis. Crucially, it is the first method capable of assessing non-factorized posteriors without assuming axis-aligned latent directions, enabling adaptive identification of the true geometric orientations of generative factors in latent space. In contrast to dominant axis-aligned metrics (e.g., DCI, MIG), our approach achieves significantly higher accuracy in recovering ground-truth factor directions on two standard benchmark datasets. By relaxing restrictive geometric assumptions, it establishes a more general, robust, and theoretically principled quantitative standard for disentanglement evaluation in DLVMs.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Deep latent variable models (DLVMs) are designed to learn meaningful representations in an unsupervised manner, such that the hidden explanatory factors are interpretable by independent latent variables (aka disentanglement). The variational autoencoder (VAE) is a popular DLVM widely studied in disentanglement analysis due to the modeling of the posterior distribution using a factorized Gaussian distribution that encourages the alignment of the latent factors with the latent axes. Several metrics have been proposed recently, assuming that the latent variables explaining the variation in data are aligned with the latent axes (cardinal directions). However, there are other DLVMs, such as the AAE and WAE-MMD (matching the aggregate posterior to the prior), where the latent variables might not be aligned with the latent axes. In this work, we propose a statistical method to evaluate disentanglement for any DLVMs in general. The proposed technique discovers the latent vectors representing the generative factors of a dataset that can be different from the cardinal latent axes. We empirically demonstrate the advantage of the method on two datasets.

Problem

• Deep Latent Variable Models
• Alignment and Disentanglement
• Performance Evaluation

Innovation

• Decoupling Performance Evaluation
• Deep Latent Variable Models
• Alignment-free Assessment