Independent Component Discovery in Temporal Count Data

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 real-world applications to gut microbiome and climate datasets reveal co-variation patterns and regime shifts consistent with domain-specific knowledge.

Temporal event counts and entity abundances are increasingly collected across domains such as microbiology and climate science. Yet, they remain challenging to analyze due to hidden patterns and regime-dependent effects. In this work, we introduce a generative framework for disentangling hidden signals in temporal count data, yielding independent sources whose contributions vary across regimes. The model is theoretically identifiable, enabling principled interpretation of the recovered components. We further develop a dedicated variational inference procedure that exploits the model’s probabilistic structure to learn its parameters efficiently. Experiments on synthetic data explore its capabilities in controlled settings, while applications to gut microbiome and climate datasets reveal meaningful co-variation patterns and regime shifts consistent with domain-specific knowledge.