The Poisson tensor completion parametric estimator

2025/05/08 by Daniel Dunlavy, Dunlavy, Daniel M., Richard B. Lehoucq +5 · 1 citation
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistics Theory (math.ST) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2505.04957

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins -- including those containing few to no samples -- and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

Citations

• A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information
• Near-Efficient and Non-Asymptotic Multiway Inference
• Multivariate Poisson intensity estimation via low-rank tensor decomposition
• Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric\n Density Estimation
• Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros
• Improving Nonparametric Density Estimation with Tensor Decompositions
• Array programming with NumPy
• Tensor Completion Made Practical
• Optimal rates of entropy estimation over Lipschitz balls
• Efficient multivariate entropy estimation via k-nearest neighbour distances
• Tensor Decompositions and Applications
• Multivariate k-nearest neighbor density estimates
• Some Mathematical Notes on Three-Mode Factor Analysis

Cited by

• A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information

Related

• Improving Nonparametric Density Estimation with Tensor Decompositions
• Multivariate Poisson intensity estimation via low-rank tensor decomposition
• Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes
• A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information
• The Average Spectrum Norm and Near-Optimal Tensor Completion