Work

Heteroskedastic Canonical Polyadic Tensor Decomposition

Year: 2026

Type: preprint

Abstract: When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.00498

Authors: Ritscher, Kyle, Llosa-Vite, Carlos

Institutions: University of California, Los Angeles, Sandia National Laboratories

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, National Nuclear Security Administration, University of California, Los Angeles, Sandia National Laboratories

Awards: G11630931, G2214935549, G413247060, G4903105778, G5339743583, G855168022

OpenAlex ID: W7215907738

Cites: 40

Cited by:

Related to: 10