The Expectation-Maximization (EM) algorithm is useful for applying the Maximum Likelihood Estimation (MLE) when there exist latent (hidden) variables in the model. However, when dealing with outliers, the expectation (mean) is not robust statistics.
Now for MLE, we can use M-estimators to reduce the effect of outliers which can be used in the M-step (maximization). My question is if there is a robust alternative for the E-step (expectation) in the EM algorithm? I'm interested in both mathematical and empirical alternatives.