  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.
