Precision medicine aims for personalized prognosis and therapeutics by utilizing recent genome-scale high-throughput profiling techniques, including next-generation sequencing (NGS). However, translating NGS data faces several challenges. First, NGS count data are often overdispersed, requiring appropriate modeling. Second, compared to the number of involved molecules and system complexity, the number of available samples for studying complex disease, such as cancer, is often limited, especially considering disease heterogeneity. The key question is whether we may integrate available data from all different sources or domains to achieve reproducible disease prognosis based on NGS count data. In this paper, we develop a Bayesian Multi-Domain Learning (BMDL) model that derives domain-dependent latent representations of overdispersed count data based on hierarchical negative binomial factorization for accurate cancer subtyping even if the number of samples for a specific cancer type is small. Experimental results from both our simulated and NGS datasets from The Cancer Genome Atlas (TCGA) demonstrate the promising potential of BMDL for effective multi-domain learning without ``negative transfer'' effects often seen in existing multi-task learning and transfer learning methods.

InMTL, there areDdifferent labeled domains where data are related and the goal is to improve the predictive power of all domains altogether.

Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors and predict future negative events, the field of quantitative behavioral research has evolved toincreasingly rely upon panel count data collected viamultiple self reports, for example, about frequencies ofsmoking using in-the-moment surveysonmobile devices. However, missing reports are common and present a major barrier to downstream statistical learning.

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.

Graphical models such as Gaussian graphical models have been widely applied for direct interaction inference in many different areas. In many modern applications, such as single-cell RNA sequencing (scRNA-seq) studies, the observed data are counts and often contain many small counts. Traditional graphical models for continuous data are inappropriate for network inference of count data. We consider the Poisson log-normal (PLN) graphical model for count data and the precision matrix of the latent normal distribution represents the network. We propose a two-step method PLNet to estimate the precision matrix. PLNet first estimates the latent covariance matrix using the maximum marginal likelihood estimator (MMLE) and then estimates the precision matrix by minimizing the lasso-penalized D-trace loss function. We establish the convergence rate of the MMLE of the covariance matrix and further establish the convergence rate and the sign consistency of the proposed PLNet estimator of the precision matrix in the high dimensional setting. Importantly, although the PLN model is not sub-Gaussian, we show that the PLNet estimator is consistent even if the model dimension goes to infinity exponentially as the sample size increases. The performance of PLNet is evaluated and compared with available methods using simulation and gene regulatory network analysis of real scRNA-seq data.

Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors and predict future negative events, the field of quantitative behavioral research has evolved to increasingly rely upon panel count data collected via multiple self reports, for example, about frequencies of smoking using in-the-moment surveys on mobile devices. However, missing reports are common and present a major barrier to downstream statistical learning. As a first step, under a missing completely at random assumption (MCAR), we propose a simple yet widely applicable functional EM algorithm to estimate the counting process mean function, which is of central interest to behavioral scientists. The proposed approach wraps several popular panel count inference methods, seamlessly deals with incomplete counts and is robust to misspecification of the Poisson process assumption. Theoretical analysis of the proposed algorithm provides finite-sample guarantees by extending parametric EM theory to the general non-parametric setting. We illustrate the utility of the proposed algorithm through numerical experiments and an analysis of smoking cessation data. We also discuss useful extensions to address deviations from the MCAR assumption and covariate effects.

Causal discovery from observational data, especially for count data, is essential across scientific and industrial contexts, such as biology, economics, and network operation maintenance.