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This paper introduces heteroskedastic-CP (HCP), a novel tensor decomposition method that extends standard CP by modeling entrywise variability through a low-rank precision tensor rather than assuming constant variance. By developing an alternating block-coordinate ascent algorithm, the authors achieve computational efficiency comparable to existing methods while demonstrating utility in synthetic tests and EEG signal analysis. This advancement represents a significant step forward in handling noisy, heterogeneous data within machine learning frameworks.
Heteroskedastic Canonical Polyadic Tensor Decomposition
arXiv:2610.00498v1 Announce Type: cross 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.
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.
Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.00498 [stat.ME]
(or arXiv:2610.00498v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2610.00498 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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