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.

本文介绍了一种修改后的矩阵变量正态分布，即均值受限制的矩阵变量正态分布，可以用于最大似然估计和缺失数据插补，特别适用于高维数据。在多元和可转置的框架中，本文提出了一种基于 EM 算法的缺失数据插补方法，并表明这种插补方法优于现有方法并具有更大的灵活性。

可转置正则协方差模型及其在缺失数据插补中的应用

Transposable regularized covariance models with an application to  missing data imputation

The estimation of missing input vector elements in real time processing
applications requires a system that possesses the knowledge of certain
characteristics such as correlations between variables, which are inherent in
the input space. Computational intelligence techniques and maximum likelihood
techniques do possess such characteristics and as a result are important for
imputation of missing data. This paper compares two approaches to the problem
of missing data estimation. The first technique is based on the current state
of the art approach to this problem, that being the use of Maximum Likelihood
(ML) and Expectation Maximisation (EM. The second approach is the use of a
system based on auto-associative neural networks and the Genetic Algorithm as
discussed by Adbella and Marwala3. The estimation ability of both of these
techniques is compared, based on three datasets and conclusions are made.

本文比较了基于最大似然和期望最大化算法（ML 和 EM）和基于自关联神经网络和遗传算法的两种方法对于缺失数据估计的能力，并基于三组数据集得出了结论。