Paper Info
Title
Concentration of the Frobenius Norm of Generalized Matrix Inverses.
Abstract
In many applications it is useful to replace the Moore-Penrose pseudoinverse (MPP) by a different generalized inverse with more favorable properties. We may want, for example, to have many zero entries, but without giving up too much of the stability of the MPP. One way to quantify stability is by how much the Frobenius norm of a generalized inverse exceeds that of the MPP. In this paper we derive finite-size concentration bounds for the Frobenius norm of l(p)-minimal general inverses of iid Gaussian matrices, with 1 <= p <= 2. For p = 1 we prove exponential concentration of the Frobenius norm of the sparse pseudoinverse; for p = 2, we get a similar concentration bound for the MPP. Our proof is based on the convex Gaussian min-max theorem, but unlike previous applications which give asymptotic results, we derive finite-size bounds.
Year
DOI
Venue
2019
10.1137/17M1145409
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Keywords
DocType
Volume
sparse pseudoinverse,random matrices,convex analysis,l(p) minimization,Frobenius norm,concentration bound
Journal
40
Issue
ISSN
Citations 
1
0895-4798
1
PageRank 
References 
Authors
0.38
0
2
Name
Order
Citations
PageRank
Ivan Dokmanic115522.37
Rémi Gribonval2120783.59