Estimation and computations for Gaussian mixtures with uniform noise under separation constraints

In this paper we study a finite Gaussian mixture model with an additional uniform component that has the role to catch points in the tails of the data distribution. An adaptive constraint enforces a certain level of separation between the Gaussian mixture components and the uniform component representing noise and outliers in the tail of the distribution. The latter makes the proposed tool particularly useful for robust estimation and outlier identification. A constrained ML estimator is introduced for which existence and consistency is shown. One of the attractive features of the methodology is that the noise level is estimated from data. We also develop an EM-type algorithm with proven convergence. Based on numerical evidence we show how the methods developed in this paper are useful for several fundamental data analysis tasks: outlier identification, robust location-scale estimation, clustering, and density estimation.

Feature compensation based on independent noise estimation for robust speech recognition

In this paper, we propose a novel feature compensation algorithm based on independent noise estimation, which employs a Gaussian mixture model (GMM) with fewer Gaussian components to rapidly estimate the noise parameters from the noisy speech and monitor the noise variation. The estimated noise model is combined with a GMM with sufficient Gaussian mixtures to produce the noisy GMM for the clean speech estimation so that parameters are updated if and only if the noise variation occurs. Experimental results show that the proposed algorithm can achieve the recognition accuracy similar to that of the traditional GMM-based feature compensation, but significantly reduces the computational cost, and thereby is more useful for resource-limited mobile devices.