# Adaptive Estimation in Two-way Sparse Reduced-rank Regression

arXiv: https://arxiv.org/abs/1403.1922 · HTML: https://mlsanity.com/paper/1403.1922/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2014.

## Built on by (most cited first, 1 of 1)

- [Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations](https://mlsanity.com/paper/2211.15889/) (2022)

## Abstract (arXiv)

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a few rows and columns. We are especially interested in the high dimensional settings where the number of predictors and/or response variables can be much larger than the number of observations. We propose a new estimation scheme, which achieves competitive numerical performance and at the same time allows fast computation. Moreover, we show that (a slight variant of) the proposed estimator achieves near optimal non-asymptotic minimax rates of estimation under a collection of squared Schatten norm losses simultaneously by providing both the error bounds for the estimator and minimax lower bounds. The effectiveness of the proposed algorithm is also demonstrated on an textitin vivo calcium imaging dataset.