Gaussian Mixture Models with Uncertain Parameters

Gaussian mixture models (GMMs) are among the most fundamental and widely used statistical models. Because of insufficient or noisy training data in real-world problems, the estimated parameters of the GMM are not able to accurately represent the underlying distributions of the observations. In this paper, we investigate the GMM with uncertain mean vector or uncertain covariance matrix. To handle uncertain parameters, we assume that they vary anywhere in an interval with uniform possibilities. As a result, the likelihood of the GMM with uncertain parameters becomes an interval rather than a precise real number. Due to interval likelihoods, the maximum-likelihood (ML) criterion is not suitable for classification. Hence we use the generalized linear model (GLM) for classification decision-making. Multi-category classification on different datasets from UCI repository shows that GMMs with uncertain parameters are better than conventional GMMs. The proposed method for modeling uncertain parameters of the GMM can be applied to other statistical models which may have uncertain parameters because of incomplete information in real-world problems.