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Sparse higher order partial least squares for simultaneous variable selection, dimension reduction, and tensor denoising

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Kwangmoon Park, Sündüz Keleş

Methodology · Submitted 13 Oct 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim SHOPS simultaneously accommodates variable selection, dimension reduction, and tensor response denoising.

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arXiv ID2310.09428 (version 2)
Pith IDIUVAWJKA, Pith's permanent record of this paper and its review
CitationKwangmoon Park, S\"und\"uz Kele\c{s}. "Sparse higher order partial least squares for simultaneous variable selection, dimension reduction, and tensor denoising." arXiv:2310.09428 (2023). https://pith.science/paper/IUVAWJKA
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What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.23 · human participants 0.15 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.91 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. As multidimensional tensor data is becoming more widespread, tensor adaptations of PLS have been developed. In this paper, we first establish the statistical behavior of Higher Order PLS (HOPLS) of Zhao et al. (2012), by showing that the consistency of the HOPLS estimator cannot be guaranteed as the tensor dimensions and the number of features increase faster than the sample size. To tackle this issue, we propose Sparse Higher Order Partial Least Squares (SHOPS) regression and an accompanying algorithm. SHOPS simultaneously accommodates variable selection, dimension reduction, and tensor response denoising. We further establish the asymptotic results of the SHOPS algorithm under a high-dimensional regime. The results also complete the unknown theoretic properties of SPLS algorithm (Chun and Kele\c{s}, 2010). We verify these findings through comprehensive simulation experiments, and application to an emerging high-dimensional biological data analysis.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. background 1.00 0.04 0.02 asserted 1.00
s1 As multidimensional tensor data is becoming more widespread, tensor adaptations of PLS have been developed. background 1.00 0.04 0.02 asserted 1.00
s2 In this paper, we first establish the statistical behavior of Higher Order PLS (HOPLS) of Zhao et al. (2012), by showing that the consistency of the HOPLS estimator cannot be guaranteed as the tensor dimensions and the number of features increase faster than the sample size. result 0.68 0.89 0.19 asserted 1.00
s3 To tackle this issue, we propose Sparse Higher Order Partial Least Squares (SHOPS) regression and an accompanying algorithm. contribution 0.91 0.93 0.15 asserted 0.99
s4 SHOPS simultaneously accommodates variable selection, dimension reduction, and tensor response denoising. contribution 0.85 0.79 0.23 asserted 1.00
s5 We further establish the asymptotic results of the SHOPS algorithm under a high-dimensional regime. contribution 0.67 0.94 0.13 asserted 1.00
s6 The results also complete the unknown theoretic properties of SPLS algorithm (Chun and Kele\c{s}, 2010). interpretation 0.37 0.78 0.09 asserted 0.99
s7 We verify these findings through comprehensive simulation experiments, and application to an emerging high-dimensional biological data analysis. contribution 0.53 0.95 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.74.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. As multidimensional tensor data is becoming more widespread, tensor adaptations of PLS have been developed. In this paper, we first establish the statistical behavior of Higher Order PLS (HOPLS) of Zhao et al. (2012), by showing that the consistency of the HOPLS estimator cannot be guaranteed as the tensor dimensions and the number of features increase faster than the sample size. To tackle this issue, we propose Sparse Higher Order Partial Least Squares (SHOPS) regression and an accompanying algorithm. SHOPS simultaneously accommodates variable selection, dimension reduction, and tensor response denoising. We further establish the asymptotic results of the SHOPS algorithm under a high-dimensional regime. The results also complete the unknown theoretic properties of SPLS algorithm (Chun and Kele\c{s}, 2010). We verify these findings through comprehensive simulation experiments, and application to an emerging high-dimensional biological data analysis.

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