Adaptive Estimation in Two-way Sparse Reduced-rank Regression [article]

Zhuang Ma, Zongming Ma, Tingni Sun
2016 arXiv   pre-print
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
more » ... rical 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 in vivo calcium imaging dataset.
arXiv:1403.1922v2 fatcat:qnoeaofavbbktobbuahrt6hf6a