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.

翻译：数据采集技术的进步正在产生日益增长的时序计数观测数据，这使得适应性建模变得越来越必要。在本研究中，我们提出了一个针对时序计数数据的独立成分分析生成框架，该框架将状态自适应的动态过程与泊松对数正态发射模型相结合。该模型能够识别具有状态依赖性贡献的解耦成分，从而实现表示学习和扰动分析。值得注意的是，我们确立了该模型的可识别性，为原理性解释提供了支持。为了学习模型参数，我们提出了一种高效的摊销变分推断方法。在模拟数据上的实验评估了不同设置下混合函数和潜在源的恢复效果，而一项体内纵向肠道微生物组研究则揭示了与临床扰动相一致的微生物共变异模式和状态转移。