# Independent Component Discovery in Temporal Count Data

arXiv: https://arxiv.org/abs/2601.21696 · HTML: https://mlsanity.com/paper/2601.21696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Amortized Inference Regularization](https://mlsanity.com/paper/1805.08913/) (2018)
- [Independent Innovation Analysis for Nonlinear Vector Autoregressive Process](https://mlsanity.com/paper/2006.10944/) (2020)
- [Faster independent component analysis by preconditioning with Hessian approximations](https://mlsanity.com/paper/1706.08171/) (2017)
- [Variational inference for sparse network reconstruction from count data](https://mlsanity.com/paper/1806.03120/) (2018)
- [Spatiotemporal wildfire modeling through point processes with moderate and extreme marks](https://mlsanity.com/paper/2105.08004/) (2021)
- [Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise](https://mlsanity.com/paper/1806.01094/) (2018)
- [Identifiable Feature Learning for Spatial Data with Nonlinear ICA](https://mlsanity.com/paper/2311.16849/) (2023)
- [Zero-inflation in the Multivariate Poisson Lognormal Family](https://mlsanity.com/paper/2405.14711/) (2024)
- [Tree-based variational inference for Poisson log-normal models](https://mlsanity.com/paper/2406.17361/) (2024)
- [Robust and Scalable Models of Microbiome Dynamics](https://mlsanity.com/paper/1805.04591/) (2018)
- [TaxaPLN: a taxonomy-aware augmentation strategy for microbiome-trait classification including metadata](https://mlsanity.com/paper/2507.03588/) (2025)

## Abstract (arXiv)

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.