Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Adaptive Estimation in Two-way Sparse Reduced-rank Regression (1403.1922v2)

Published 8 Mar 2014 in stat.ME, math.ST, and stat.TH

Abstract: 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 \textit{in vivo} calcium imaging dataset.

Summary

We haven't generated a summary for this paper yet.