A Robust High-Dimensional Estimation of Multinomial Mixture Models

In this paper, we are concerned with a robustifying high-dimensional (RHD) structured estimation in finite mixture of multinomial models. This method has been used in many applications that often involve outliers and data corruption. Thus, we introduce a class of the multinomial logistic mixture models for dependent variables having two or more discrete categorical levels. Through the optimization with the expectation maximization (EM) algorithm, we study two distinct ways to overcome sparsity in finite mixture of the multinomial logistic model; i.e., in the parameter space, or in the output space. It is shown that the new method is consistent for RHD structured estimation. Finally, we will implement the proposed method on real data.