Riemannian Optimization for Non-centered Mixture of Scaled Gaussian Distributions

This paper studies the statistical model of non-centered mixture scaled Gaussian distributions (NC-MSG). Using Fisher-Rao information geometry associated with this distribution, we derive a Riemannian gradient descent algorithm. algorithm is leveraged for two minimization problems. The first regularized negative log-likelihood (NLL). latter makes trade-off between white distribution and NC-MSG. Conditions on regularization are given so that existence minimum to problem guaranteed without assumptions samples. Then, Kullback-Leibler (KL) divergence NC-MSG derived. enables us define second problem. computation centers mass several NC-MSGs. Numerical experiments show good performance speed Finally, Nearest centrol̎d classifier implemented leveraging KL its center mass. Applied large-scale dataset xmlns:xlink="http://www.w3.org/1999/xlink">Breizhcrops , classifier shows accuracies robustness rigid transformations test set.