In this work, we focus on two things: First, in addition to the data measurement uncertainty, we develop a novel probabilistic model by imposing the additive noise in the classical fuzzy regression model. We obtain the baseline LS estimation as the maximum likelihood estimation for regression parameters. Moreover, by assuming the heavy tail distribution and by introducing the Huber norm instead of square in the cost function, we obtain more general robust fuzzy M-estimator, much more suitable for modeling the outliers often present in the data sets.

The paper presents a novel precision matrix modeling technique for Gaussian Mixture Models (GMMs), which is based on the concept of sparse representation. Representation coefficients of each precision matrix (inverse covariance), as well as an accompanying overcomplete matrix dictionary, are learned by minimizing an appropriate functional, the first component of which corresponds to the sum of Kullback-Leibler (KL) divergences between the initial and the target GMM, and the second represents the sparse regularizer of the coefficients. Compared to the existing, alternative approaches for approximate GMM modeling, like popular subspace-based representation methods, the proposed model results in notably better trade-off between the representation error and the computational (memory) complexity. This is achieved under assumption that the training data in the recognition system utilizing GMM have an inherent sparseness property, which enables application of the proposed model and approximate representation using only one dictionary and a significantly smaller number of coefficients. Proposed model is experimentally compared with the Subspace Precision and Mean (SPAM) model, a state of the art instance of subspace-based representation models, using both the data from a real Automatic Speech Recognition (ASR) system, and specially designed sets of artificially created/synthetic data.