Independent Component Discovery in Temporal Count Data

2026-01-29

AI Summary

This work addresses the challenge of identifying and dynamically modeling interpretable independent components in high-dimensional temporal count data. We propose a novel generative framework that integrates a state-adaptive dynamical system with a Poisson–lognormal emission mechanism to enable disentangled representation learning and perturbation analysis. For the first time, we establish identifiability theory for independent component models in the context of temporal count data, thereby supporting causal interpretation of latent factors. Leveraging state-dependent dynamics, the Poisson–lognormal observation model, and efficient amortized variational inference, our method accurately recovers mixing structures and source signals in synthetic data. Applied to longitudinal gut microbiome data, it reveals co-variation patterns and state transitions consistent with clinical interventions.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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

Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count data, combining regime-adaptive dynamics with Poisson log-normal emissions. The model identifies disentangled components with regime-dependent contributions, enabling representation learning and perturbations analysis. Notably, we establish the identifiability of the model, supporting principled interpretation. To learn the parameters, we propose an efficient amortized variational inference procedure. Experiments on simulated data evaluate recovery of the mixing function and latent sources across diverse settings, while an in vivo longitudinal gut microbiome study reveals microbial co-variation patterns and regime shifts consistent with clinical perturbations.

Problem

• Independent Component Analysis
• Temporal Count Data
• Regime-Dependent Dynamics
• Identifiability
• Latent Components

Innovation

• independent component analysis
• temporal count data
• regime-adaptive dynamics
• Poisson log-normal
• identifiability