Regularized TLS-EM for estimating missing data

The expectation-maximization (EM) algorithm is a widely-used statistical computation method when dealing with incomplete-data problems. Estimating missing values is one of its common applications. Based on the regression method, the total least squares (TLS) are utilized as an alternative method of original least squares. The TLS method considers errors from both explanatory variables and response variables and performs better optimization results, in order to have better estimations. We also illuminate that the optimal function of total least squares (TLS) could be proved to be the spectral norm instead of the Frobenius norm, in certain conditions. Besides, the new algorithm will include \(L_1\) $L_1$ regularization for more sparsity so that the redundant explanatory variables can be recognized. Finally, we show the effect of the new algorithm, with a series of numerical examples demonstrated.