No. 1063

Title:

Estimation of positive semidefinite correlation matrices by using convex quadratic SDP

Author(s):

Fushiki, Tadayoshi (The Institute of Statistical Mathematics)

Key words:

Bootstrap; Correlation; Convex optimization; Positive definite kernel

Abstract:

    Collaborative filtering systems are used to predict future ratings of items by users based on their past ratings. GroupLens is one of the famous collaborative filtering systems. It uses correlation between users, but the estimated correlation matrix sometimes has a serious defect: It is not positive semidefinite because not all ratings are observed. When the estimated correlation matrix is used as a Gram matrix of kernel methods, it sometimes provides a poor prediction because of the indefiniteness. Then, a positive semidefinite correlation matrix is required in such a case. In this paper, a method using a convex optimization technique is proposed to obtain a positive semidefinite correlation matrix. Recently, the nearest correlation matrix problem has been studied in the field of optimization. It is shown that the problem formulated with the information on the variances of the estimated correlation coefficients is solved by a convex quadratic semidefinite program. MovieLens dataset is used to confirm the effectiveness of the proposed method.