Rank-Constrained Least-Squares: Prediction and Inference

11/29/2021
by   Michael Law, et al.
0

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on the design matrix. Lying at the heart of the proof is a covering number bound for the family of projection operators corresponding to the subspaces spanned by the design. By leveraging this complexity result, we perform a power analysis for a permutation test on the existence of a low-rank signal under the high-dimensional trace regression model. Finally, we use alternating minimization to approximately solve the rank-constrained least-squares problem to evaluate its empirical in-sample prediction risk and power of the resulting permutation test in our numerical study.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/12/2020

Outlier-robust sparse/low-rank least-squares regression and robust matrix completion

We consider high-dimensional least-squares regression when a fraction ϵ ...
research
07/04/2016

A Residual Bootstrap for High-Dimensional Regression with Near Low-Rank Designs

We study the residual bootstrap (RB) method in the context of high-dimen...
research
07/02/2020

Partial Trace Regression and Low-Rank Kraus Decomposition

The trace regression model, a direct extension of the well-studied linea...
research
03/08/2023

Two-sided Matrix Regression

The two-sided matrix regression model Y = A^*X B^* +E aims at predicting...
research
12/20/2017

A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm

We consider the problem of learning a high-dimensional but low-rank matr...
research
05/04/2021

Nonparametric Trace Regression in High Dimensions via Sign Series Representation

Learning of matrix-valued data has recently surged in a range of scienti...
research
04/29/2021

A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression

Low-rank tensors are an established framework for high-dimensional least...

Please sign up or login with your details

Forgot password? Click here to reset