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We propose a new and computationally efficient algorithm for maximizing theobserved log-likelihood for a multivariate normal data matrix with missingvalues. We show that our procedure based on iteratively regressing the missingon the observed variables, generalizes the standard EM algorithm by alternatingbetween different complete data spaces and performing the E-Step incrementally.In this non-standard setup we prove numerical convergence to a stationary pointof the observed log-likelihood.  For high-dimensional data, where the number of variables may greatly exceedsample size, we add a Lasso penalty in the regression part of our algorithm andperform coordinate descent approximations. This leads to a computationally veryattractive technique with sparse regression coefficients for missing dataimputation. Simulations and results on four microarray datasets show that thenew method often outperforms other imputation techniques as k-nearest neighborsimputation, nuclear norm minimization or a penalized likelihood approach withan l1-penalty on the inverse covariance matrix.

Pattern Alternating Maximization Algorithm for Missing Data in Large P, Small N Problems