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On Cross-validation for Sparse Reduced Rank Regression

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Yiyuan She, Hoang Tran

Methodology · Submitted 30 Dec 2018

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

The authors' main claim However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate.

how it is stated · asserted 0.88 read the record →

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arXiv ID1812.11555 (version 1)
Pith IDR3ZR6AYH, Pith's permanent record of this paper and its review
CitationHoang Tran, Yiyuan She. "On Cross-validation for Sparse Reduced Rank Regression." arXiv:1812.11555 (2018). https://pith.science/paper/R3ZR6AYH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,916 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.19 · human participants 0.03 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.35 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. Our in-sample error studies in jointly sparse and rank-deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. By use of an identity, we propose a novel scale-free calibration to help cross-validation achieve the minimax optimal error rate non-asymptotically. Experiments support the efficacy of the proposed methods.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. background 1.00 0.04 0.02 asserted 1.00
s1 To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. background 0.97 0.06 0.03 asserted 0.98
s2 However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. contribution 0.70 0.90 0.68 asserted 0.88
s3 Our in-sample error studies in jointly sparse and rank-deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. contribution 0.79 0.96 0.12 asserted 1.00
s4 By use of an identity, we propose a novel scale-free calibration to help cross-validation achieve the minimax optimal error rate non-asymptotically. contribution 0.61 0.94 0.16 asserted 0.94
s5 Experiments support the efficacy of the proposed methods. result 0.96 0.89 0.16 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from simulation or computation 0.76.

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  • references and citing sentences
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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

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. Our in-sample error studies in jointly sparse and rank-deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. By use of an identity, we propose a novel scale-free calibration to help cross-validation achieve the minimax optimal error rate non-asymptotically. Experiments support the efficacy of the proposed methods.

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