Zero-inflated modeling with smoothing on counting tensors

TL;DR

This paper introduces a probabilistic framework for modeling sparse, zero-inflated count tensors, specifically applied to single-cell Hi-C data, capturing complex dependencies and heterogeneity.

Contribution

It develops a zero-inflated Poisson tensor model combining low-rank structure, clustering, and smoothness, with a Bayesian inference method and theoretical guarantees.

Findings

Improved zero detection in single-cell Hi-C data

Enhanced latent structure recovery and clustering accuracy

Demonstrated effectiveness in 3D chromatin organization inference

Abstract

We propose a unified probabilistic framework for sparse count tensors with excess zeros, motivated by single-cell Hi-C data. The observed data are naturally represented as a three-way tensor indexed by genomic loci pairs and cells, exhibiting pronounced sparsity, zero inflation, and cell-to-cell heterogeneity. We introduce a zero-inflated Poisson tensor model that integrates low-rank CP structure, cluster-specific latent embeddings, and smoothness along ordered genomic loci, thereby jointly capturing multiway dependence, heterogeneity, and structured variation. We develop a Bayes-optimal procedure for distinguishing structural from technical zeros, enabling principled inference and uncertainty quantification. We establish identifiability of the model parameters and derive consistency rates for the proposed estimators in a high-dimensional regime. Simulation studies and analyses of single-cell Hi-C data demonstrate improved performance in zero detection, latent structure recovery, and downstream tasks such as clustering and 3D chromatin organization inference. The proposed framework provides a flexible approach for multiway count data with excess zeros and structured dependencies, and suggests several directions for future work, including mixture-based modeling of cell populations and scalable computation for large-scale applications.