Transposable regularized covariance models with an application to missing data imputation

TL;DR

This paper introduces transposable regularized covariance models for high-dimensional missing data imputation, leveraging a modified matrix-variate normal distribution with separate row and column covariances, and demonstrates their effectiveness through simulations and real data applications.

Contribution

It proposes a novel transposable regularized covariance model and EM algorithms for missing data imputation, extending matrix-variate normal models to high-dimensional settings.

Findings

Models outperform existing imputation methods.

Applicable to high-dimensional microarray and Netflix data.

Flexible and theoretically grounded approach.

Abstract

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so-called transposable regularized covariance models allow for maximum likelihood estimation of the mean and nonsingular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.