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arxiv: 2604.22088 · v1 · submitted 2026-04-23 · 📊 stat.ME · stat.AP

Zero-inflated modeling with smoothing on counting tensors

Elena Tuzhilina , Yaoming Zhen This is my paper

Pith reviewed 2026-05-09 20:32 UTC · model grok-4.3

classification 📊 stat.ME stat.AP
keywords zero-inflated Poissontensor decompositionsingle-cell Hi-Clow-rank CPstructural zerosidentifiabilityconsistency ratesgenomic smoothness
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The pith

A zero-inflated Poisson tensor model with low-rank CP structure and smoothness separates structural from technical zeros in sparse count data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a probabilistic model for three-way count tensors that have many zeros, as seen in single-cell Hi-C experiments measuring interactions between genomic loci across cells. It combines a zero-inflated Poisson distribution with a low-rank canonical polyadic decomposition, latent cluster embeddings for cells, and smoothing constraints along the ordered genomic positions. This setup allows a Bayes-optimal way to tell apart biologically meaningful structural zeros from technical artifacts due to measurement limits, while providing uncertainty measures and consistent parameter estimates in high dimensions. The approach is shown to enhance zero detection and recover latent patterns better than alternatives in simulations and real data, supporting tasks like cell clustering and 3D chromatin structure inference.

Core claim

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.

What carries the argument

Zero-inflated Poisson tensor model that combines low-rank CP decomposition with cluster-specific latent embeddings and smoothness along genomic loci to model the mean and separate zero types.

If this is right

  • Model parameters are identifiable under the stated assumptions.
  • Proposed estimators achieve consistency rates in high-dimensional regimes.
  • The procedure improves zero detection accuracy and latent structure recovery compared to alternatives.
  • Outputs support better performance on downstream tasks including cell clustering and 3D chromatin organization inference.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same tensor modeling approach could apply directly to other multiway sparse count data with excess zeros and ordered indices outside genomics.
  • Future mixture extensions for cell populations would address additional layers of heterogeneity without changing the core zero-inflation mechanism.
  • Scalable approximations or tensor sketching would be required to scale the method beyond current single-cell Hi-C dataset sizes.

Load-bearing premise

The observed count tensor is generated from a zero-inflated Poisson whose mean structure exactly matches a low-rank CP decomposition that includes cluster embeddings and smoothness along ordered loci.

What would settle it

Simulated data generated from a mean structure that violates the low-rank CP plus smoothness assumption, where the Bayes-optimal zero separation rule performs no better than random classification on held-out tensors.

Figures

Figures reproduced from arXiv: 2604.22088 by Elena Tuzhilina, Yaoming Zhen.

Figure 1
Figure 1. Figure 1: Averaged relative errors achieved by various initialization methods over 50 simu [PITH_FULL_IMAGE:figures/full_fig_p027_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance of the fitting procedure as the number of cells [PITH_FULL_IMAGE:figures/full_fig_p029_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ARI vs. number of clusters R for different recovered quantities. Different panels represent different sparsity levels. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance of ZITS on the human’s single-cell Hi-C dataset. Left: ARI versus embedding dimension L for chromosome 1, averaged over 10 subsamples. Right: ARI distri￾butions across chromosomes with L = 10. We next compare ZITS with two structural-zero-aware imputation methods, HiCImpute (Xie et al., 2022) and scHiCSRS (Xu et al., 2022). We use the publicly available R im￾plementations of both methods and ru… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of ZITS with competing methods using ARI. Diamonds indicate the mean ARI over 10 subsamples. Left: count-based imputation methods that detect structural zeros. Middle: imputation methods for binarized contact matrices. Right: performance based on cell embeddings. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance of the fitting procedure as the number of clusters [PITH_FULL_IMAGE:figures/full_fig_p039_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of embeddings obtained via ZITS and CP chromosome 3. 39 [PITH_FULL_IMAGE:figures/full_fig_p039_7.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper proposes 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. It introduces 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. A Bayes-optimal procedure is developed for distinguishing structural from technical zeros, enabling principled inference and uncertainty quantification. The authors 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.

Significance. If the identifiability and consistency results are established as claimed, this work offers a valuable contribution to statistical modeling of multiway count data with excess zeros and structured dependencies. The integration of tensor factorization, clustering via latent embeddings, and smoothness priors is well-motivated for genomic applications like single-cell Hi-C. The Bayes-optimal zero classification procedure is a notable feature for handling the distinction between structural and technical zeros. The empirical validation supports the practical utility of the approach.

minor comments (2)
  1. The abstract is quite dense; consider breaking it into shorter sentences for improved readability.
  2. More details on the specific form of the smoothness penalty or prior along genomic loci would aid in understanding the model's implementation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our work on the zero-inflated Poisson tensor model for sparse count tensors, as well as for recommending minor revision. We are pleased that the integration of CP structure, latent embeddings, smoothness, Bayes-optimal zero classification, identifiability, and consistency results is viewed as a valuable contribution to statistical modeling of multiway count data.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's abstract and summary present a zero-inflated Poisson tensor model with CP structure, embeddings, and smoothness, along with claims of identifiability and consistency rates derived under stated assumptions. No equations, self-citations, or derivations are visible that reduce predictions to fitted inputs by construction. The theoretical results are positioned as independent contributions based on the model matching the data-generating process, with no load-bearing steps that collapse to self-definition or renaming. This is the standard case of a self-contained probabilistic framework without internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the model implicitly assumes a zero-inflated Poisson generative process, low-rank CP structure, cluster embeddings, and genomic smoothness, but none are quantified or justified here.

pith-pipeline@v0.9.0 · 5486 in / 1453 out tokens · 37512 ms · 2026-05-09T20:32:54.684616+00:00 · methodology

discussion (0)

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Reference graph

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