Sparse multivariate regression with missing values and its application to the prediction of material properties

TL;DR

This paper introduces a sparse multivariate regression method with an EM algorithm to handle missing data, improving prediction of material properties by incorporating response variable correlations.

Contribution

It proposes a penalized maximum likelihood approach with $l_1$-regularization and an EM algorithm for sparse estimation in multivariate regression with missing values.

Findings

Effective in predicting material properties with missing data

Incorporates correlation structure among responses

Applied successfully to real material data

Abstract

In the field of materials science and engineering, statistical analysis and machine learning techniques have recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. This study conducts a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ $l_1$-regularization to achieve a sparse estimation of regression coefficients and the inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in response variables, owing to the difficulty in collecting data on material properties. A method to improve prediction accuracy under the situation with missing values incorporates a correlation structure among the response variables into the statistical model. The expectation and maximization algorithm is constructed, which enables application to a data set with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties.