# On Cross-validation for Sparse Reduced Rank Regression

arXiv: https://arxiv.org/abs/1812.11555 · HTML: https://mlsanity.com/paper/1812.11555/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2018.

## Built on by (most cited first, 6 of 6)

- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction](https://mlsanity.com/paper/2112.09746/) (2021)
- [Slow Kill for Big Data Learning](https://mlsanity.com/paper/2305.01726/) (2023)
- [Knowledge-Embedded Latent Projection for Robust Representation Learning](https://mlsanity.com/paper/2602.16709/) (2026)
- [Generalized Information Criteria for Structured Sparse Models](https://mlsanity.com/paper/2309.01764/) (2023)
- [Range Penalization: Theoretical Insights with Applications in Federated Learning](https://mlsanity.com/paper/2606.10916/) (2026)

## Abstract (arXiv)

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.