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.

翻译：随着数据采集技术的进步，时间计数观测数据日益增多，对适应性建模的需求也随之提升。本文提出了一种针对时间计数数据的独立成分分析生成框架，将机制自适应动力学与泊松对数正态发射模型相结合。该模型能够识别具有机制依赖贡献的解耦成分，从而实现表征学习与扰动分析。值得注意的是，我们建立了模型的可辨识性，为原则性解释提供支撑。为学习参数，我们提出了一种高效的分摊变分推断程序。在模拟数据上的实验评估了不同设置下混合函数与潜在源的恢复效果，而对肠道微生物组与气候数据集的真实应用则揭示了与领域知识一致的变化模式与机制转移。