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Title: Adaptive Reduced Rank Regression
We study the low rank regression problem y = Mx + ε, where x and y are d1 and d2 dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations n is less than d1 + d2. Existing algorithms are designed for settings where n is typically as large as rank(M)(d1+d2). This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix de-noising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baseline, and is always at least competitive.  more » « less
Award ID(s):
1942680 1952085
PAR ID:
10225175
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Advances in neural information processing systems
ISSN:
1049-5258
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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