Independent Component Discovery in Temporal Count Data

TL;DR

This paper introduces a generative model for analyzing temporal count data, enabling the discovery of independent components with regime-dependent dynamics, supported by theoretical identifiability and efficient inference, demonstrated on simulated and real microbiome data.

Contribution

It presents a novel regime-adaptive ICA framework for temporal count data with proven identifiability and an efficient inference method, advancing interpretability and analysis of complex temporal datasets.

Findings

Successful recovery of latent sources in simulations

Identification of microbial co-variation patterns

Detection of regime shifts aligned with clinical perturbations

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.