A0642
Title: Penalized likelihood approach in multivariate regression with missing values and its application to materials science
Authors: Kei Hirose - Kyushu University (Japan) [presenting]
Keisuke Teramoto - Hiroshima University (Japan)
Abstract: In the field of materials science and engineering, statistical analysis has recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. We conduct a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ L1 regularization to achieve a sparse estimation of regression coefficients and inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in the response variables, owing to the difficulty of collecting data on material properties. We, therefore, propose a method that incorporates a correlation structure among the response variables into a statistical model to improve the prediction accuracy. The expectation-maximization (EM) algorithm is constructed, which allows the application to a dataset with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties.
