# Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction

arXiv: https://arxiv.org/abs/2112.09746 · HTML: https://mlsanity.com/paper/2112.09746/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 55 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 5 of 5)

- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [On Cross-validation for Sparse Reduced Rank Regression](https://mlsanity.com/paper/1812.11555/) (2018)
- [Analysis of Generalized Bregman Surrogate Algorithms for Nonsmooth Nonconvex Statistical Learning](https://mlsanity.com/paper/2112.09191/) (2021)
- [AMOS: An Automated Model Order Selection Algorithm for Spectral Graph Clustering](https://mlsanity.com/paper/1609.06457/) (2016)
- [Indirect Gaussian Graph Learning beyond Gaussianity](https://mlsanity.com/paper/1610.02590/) (2016)

## Built on by (most cited first, 3 of 3)

- [Coefficient Shape Alignment in Multiple Functional Linear Regression](https://mlsanity.com/paper/2312.01925/) (2023)
- [Coefficient Shape Transfer Learning for Functional Linear Regression](https://mlsanity.com/paper/2506.11367/) (2025)
- [Range Penalization: Theoretical Insights with Applications in Federated Learning](https://mlsanity.com/paper/2606.10916/) (2026)

## Abstract (arXiv)

Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel clustered reduced-rank learning (CRL) framework that imposes two joint matrix regularizations to automatically group the features in constructing predictive factors. CRL is more interpretable than low-rank modeling and relaxes the stringent sparsity assumption in variable selection. In this paper, new information-theoretical limits are presented to reveal the intrinsic cost of seeking for clusters, as well as the blessing from dimensionality in multivariate learning. Moreover, an efficient optimization algorithm is developed, which performs subspace learning and clustering with guaranteed convergence. The obtained fixed-point estimators, though not necessarily globally optimal, enjoy the desired statistical accuracy beyond the standard likelihood setup under some regularity conditions. Moreover, a new kind of information criterion, as well as its scale-free form, is proposed for cluster and rank selection, and has a rigorous theoretical support without assuming an infinite sample size. Extensive simulations and real-data experiments demonstrate the statistical accuracy and interpretability of the proposed method.