Regularized Mixture Density Estimation With an Analytical Setting of Shrinkage Intensities

In this paper, we propose a method for
$P$
-variate probability density estimation assuming a Gaussian mixture model (GMM). Our method exploits a regularization technique for improving the estimation accuracy of the GMM component covariance matrices. We derive an expectation maximization algorithm for fitting our regularized GMM (RGMM), which exploits an analytical Ledoit–Wolf-type shrinkage estimation of the covariance matrices. Our method is compared with recent model-based and variational Bayes approximation methods using synthetic and real data sets. The obtained results show that the proposed RGMM method achieves a significant improvement in the performance of multivariate probability density estimation with respect to other methods on both the synthetic and the real data sets.