PreprintarXiv licencearXiv
Heteroskedastic Canonical Polyadic Tensor Decomposition
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.
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BibTeX
@misc{ritscher2026heteroskedastic,
title = {{Heteroskedastic Canonical Polyadic Tensor Decomposition}},
author = {Kyle Ritscher and Carlos Llosa-Vite},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00498},
eprint = {2610.00498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00498},
}
RIS
TY - UNPB
TI - Heteroskedastic Canonical Polyadic Tensor Decomposition
AU - Kyle Ritscher
AU - Carlos Llosa-Vite
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.00498
UR - https://arxiv.org/abs/2610.00498
AB - 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.
ER -