TY - GEN
T1 - On the convexity in Kronecker structured covariance estimation
AU - Wiesel, Ami
PY - 2012
Y1 - 2012
N2 - A classical model for the covariance of a random matrix is the Kronecker product of two smaller covariance matrices associated with the rows and columns. Maximum likelihood estimation in such structures involves a non-convex optimization problem and is traditionally handled via an alternating maximization Flip-Flop technique. We prove that the problem is actually geodesically convex on the manifold of positive definite matrices. This allows for better analysis, efficient numerical solutions, and simple extensions through the use of additional geodesically convex regularizations. As an example, we propose to shrink the solution towards the identity when the number of samples is insufficient. We demonstrate the advantages of this approach using computer simulations.
AB - A classical model for the covariance of a random matrix is the Kronecker product of two smaller covariance matrices associated with the rows and columns. Maximum likelihood estimation in such structures involves a non-convex optimization problem and is traditionally handled via an alternating maximization Flip-Flop technique. We prove that the problem is actually geodesically convex on the manifold of positive definite matrices. This allows for better analysis, efficient numerical solutions, and simple extensions through the use of additional geodesically convex regularizations. As an example, we propose to shrink the solution towards the identity when the number of samples is insufficient. We demonstrate the advantages of this approach using computer simulations.
KW - Geodesic convexity
KW - Kronecker
KW - covariance estimation
KW - log-sum-exp
UR - http://www.scopus.com/inward/record.url?scp=84868254293&partnerID=8YFLogxK
U2 - 10.1109/SSP.2012.6319848
DO - 10.1109/SSP.2012.6319848
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84868254293
SN - 9781467301831
T3 - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012
SP - 880
EP - 883
BT - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012
T2 - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012
Y2 - 5 August 2012 through 8 August 2012
ER -