On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies

2026-01-06

AI Summary

This work addresses the parameter non-identifiability issue in recurrent switching mechanisms (RSM) within deep latent variable time-series models by establishing a unified theoretical framework that encompasses both Markov switching models and switched dynamical systems. By integrating temporally structured finite mixture modeling, architectural constraints on neural networks, noise assumptions, and variational inference, the study provides the first identifiability guarantees—under a nonlinear Gaussian setting—for the number of regimes, transition structure, latent variables, and causal graphs, even with multiple lags. The proposed approach demonstrates its effectiveness in enhancing model interpretability and credibility across real-world datasets from neuroscience, finance, and climate science, thereby offering a reliable foundation for scientific discovery.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• 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

Abstract

Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

Problem

• Identifiability
• Regime-Switching Models
• Multi-Lag Dependencies
• Latent Variable Models
• Time Series

Innovation

• Identifiability
• Regime-Switching Models
• Multi-Lag Dependencies
• Switching Dynamical Systems
• Unsupervised Learning