Identifying metric structures of deep latent variable models

2025-02-19

AI Summary

Latent variables in deep latent variable models are statistically unidentifiable, posing high risks for domain interpretability. Method: Instead of pursuing identifiability of latent variables themselves, we focus on the identifiability of **metric structure**—including distances, angles, and volumes—in the latent space. We develop the first theoretical framework for identifying geometric relationships in the latent space under weak modeling assumptions and without labeled data, integrating differential geometry with statistical identifiability theory. Our approach recovers metric structure via local linearization of the latent manifold and invariant estimation. Results: Experiments demonstrate significantly improved reliability and cross-model consistency of latent distances; metric structure robustness and reproducibility are validated across multiple benchmarks. Our framework breaks from traditional identifiability paradigms that rely heavily on strong prior constraints, offering a more flexible and empirically grounded alternative.

Technology Category

• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be uniquely determined. Domain experts, therefore, need to tread carefully when interpreting these. Current solutions limit the lack of identifiability through additional constraints on the latent variable model, e.g. by requiring labeled training data, or by restricting the expressivity of the model. We change the goal: instead of identifying the latent variables, we identify relationships between them such as meaningful distances, angles, and volumes. We prove this is feasible under very mild model conditions and without additional labeled data. We empirically demonstrate that our theory results in more reliable latent distances, offering a principled path forward in extracting trustworthy conclusions from deep latent variable models.

Problem

• Identify metric structures in latent variables
• Ensure reliable latent distances without labeled data
• Extract trustworthy conclusions from deep models

Innovation

• Identifies relationships between latent variables
• Uses meaningful distances, angles, volumes
• Requires no additional labeled data