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Generalized multilinear models for sufficient dimension reduction on tensor-valued predictors

Daniel Kapla & Efstathia Bura

Annals of Statistics2026https://doi.org/10.1214/25-aos2598article
AJG 4*ABDC A*
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0.50

What the paper says

We consider supervised learning problems with tensor-valued input. We derive multilinear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the predictors given the response as a member of the quadratic exponential family. We develop estimation procedures of sufficient reductions for both continuous and binary tensor-valued predictors. We prove the consistency and asymptotic normality of the estimated sufficient reduction using manifold theory. For multilinear normal predictors, the estimation algorithm is highly computationally efficient and is also applicable to situations where the dimension of the reduction exceeds the sample size. Our method outperforms competing techniques in both simulated settings and real-world datasets involving continuous and binary tensor-valued predictors.

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https://doi.org/https://doi.org/10.1214/25-aos2598

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@article{daniel2026,
  title        = {{Generalized multilinear models for sufficient dimension reduction on tensor-valued predictors}},
  author       = {Daniel Kapla & Efstathia Bura},
  journal      = {Annals of Statistics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aos2598},
}

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Generalized multilinear models for sufficient dimension reduction on tensor-valued predictors

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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