Statistics Seminar（2014-12）

Topic:Precision Matrix Estimation by Inverse Principal Orthogonal Decomposition

Speaker:Cheng Yong Tang, University of Colorado Denver

Time:Monday, 23 June, 16:00-17:00

Location:Room K02, Guanghua Building 2

Abstract:We consider a parsimonious approach for modeling a large precision matrix in a factor model setting. The approach is developed by inverting a principal orthogonal decomposition (IPOD) that disentangles the systematic component from the idiosyncratic component in the target dynamic system of interest. In the IPOD approach, the impact due to the systematic component is captured by a low-dimensional factor model. Motivated by practical considerations for parsimonious and interpretable methods, we propose to use a sparse precision matrix to capture the contribution from the idiosyncratic component to the variation in the target dynamic system. Conditioning on the factors, the IPOD approach has an appealing practical interpretation in the conventional graphical models for in formatively investigating the associations between the idiosyncratic components. We discover that the large precision matrix depends on the idiosyncratic component only through its sparse precision matrix, and show that IPOD is convenient and feasible for estimating the large precision matrix in which only inverting a low-dimensional matrix is involved. We formally establish the estimation error bounds of the IPOD approach under various losses and find that the impact due to the common factors vanishes as the dimensionality of the precision matrix diverges. Extensive numerical examples including real data examples in practical problems demonstrate the merits of the IPOD approach in its performance and interpretability. This is a joint work with Yingying Fan.