Robust Model Selection for Discovery of Latent Mechanistic Processes

2026-02-25

AI Summary

This work addresses the challenge of accurately estimating the number of latent processes with mechanistic interpretability under model misspecification, where existing approaches exhibit critical limitations: likelihood-based methods tend to overestimate, while nonparametric techniques are overly conservative. To overcome this, the authors propose the Accumulated Component-wise Difference Criterion (ACDC), a novel framework that leverages component-level discrepancy measures to capture underlying mechanistic structure. ACDC delivers robust and reliable estimation of the unknown number of latent mechanisms, applicable to both supervised and unsupervised variants of latent variable models—including probabilistic matrix factorization and mixture models. Notably, this paper establishes the first consistency theory for robust model selection in this context. Empirical evaluations demonstrate that ACDC substantially outperforms current methods across diverse scenarios, consistently recovering interpretable latent mechanistic structures.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

When learning interpretable latent structures using model-based approaches, even small deviations from modeling assumptions can lead to inferential results that are not mechanistically meaningful. In this work, we consider latent structures that consist of $K_o$ mechanistic processes, where $K_o$ is unknown. When the model is misspecified, likelihood-based model selection methods can substantially overestimate $K_o$ while more robust nonparametric methods can be overly conservative. Hence, there is a need for approaches that combine the sensitivity of likelihood-based methods with the robustness of nonparametric ones. We formalize this objective in terms of a robust model selection consistency property, which is based on a component-level discrepancy measure that captures the mechanistic structure of the model. We then propose the accumulated cutoff discrepancy criterion (ACDC), which leverages plug-in estimates of component-level discrepancies. To apply ACDC, we develop mechanistically meaningful component-level discrepancies for a general class of latent variable models that includes unsupervised and supervised variants of probabilistic matrix factorization and mixture modeling. We show that ACDC is robustly consistent when applied to unsupervised matrix factorization and mixture models. Numerical results demonstrate that in practice our approach reliably identifies a mechanistically meaningful number of latent processes in numerous illustrative applications, outperforming existing methods.

Problem

• robust model selection
• latent mechanistic processes
• model misspecification
• component-level discrepancy
• model selection consistency

Innovation

• robust model selection
• latent mechanistic processes
• component-level discrepancy
• accumulated cutoff discrepancy criterion
• model misspecification