mlsanityData to 14 Oct 2026

Heteroskedastic Canonical Polyadic Tensor Decomposition

arXiv 2610.00498 ↗First posted 30 Sep 2026stat.ME cs.LG stat.MLcited by 0

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Abstract (arXiv)

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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References · 14

  1. 2020An Optimal Statistical and Computational Framework for Generalized Tensor Estimationcited by 39
  2. 2018Generalized Canonical Polyadic Tensor Decompositioncited by 34
  3. 2018Heteroskedastic PCA: Algorithm, Optimality, and Applicationscited by 34
  4. 2021Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependencecited by 12
  5. 2020Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of Variancecited by 10
  6. 2021On Estimating Rank-One Spiked Tensors in the Presence of Heavy Tailed Errorscited by 10
  7. 2021HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noisecited by 8
  8. 2021Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticitycited by 8
  9. 2023Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCAcited by 7
  10. 2024Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methodscited by 5
  11. 2014Tensor Generalized Estimating Equations for Longitudinal Imaging Analysiscited by 4
  12. 2016Towards a Theoretical Analysis of PCA for Heteroscedastic Datacited by 3
2 more
  1. 2024Statistical Inference for Low-Rank Tensors: Heteroskedasticity, Subgaussianity, and Applicationscited by 3
  2. 2026Near-Universal Multiplicative Updates for Nonnegative Einsum Factorizationcited by 2

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