Solving general elliptical mixture models through an approximate Wasserstein manifold

We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides a more desirable optimisation space. We thus provide a stable solution to the EMMs that is both robust to initialisations and reaches a superior optimum by adaptively optimising along a manifold of an approximate Wasserstein distance. To this end, we first provide a unifying account of computable and identifiable EMMs, which serves as a basis to rigorously address the underpinning optimisation problem. Due to a probability constraint, solving this problem is extremely cumbersome and unstable, especially under the Wasserstein distance. To relieve this issue, we introduce an efficient optimisation method on a statistical manifold defined under an approximate Wasserstein distance, which allows for explicit metrics and computable operations, thus significantly stabilising and improving the EMM estimation. We further propose an adaptive method to accelerate the convergence. Experimental results demonstrate the excellent performance of the proposed EMM solver.Comment: This work has been accepted to AAAI2020. Note that this version also corrects a small error on the Equation (16) in proo

Sequential Estimation for Mixture of Regression Models for Heterogeneous Population

Heterogeneity among patients commonly exists in clinical studies and leads to challenges in medical research. It is widely accepted that there exist various sub-types in the population and they are distinct from each other. The approach of identifying the sub-types and thus tailoring disease prevention and treatment is known as precision medicine.The mixture model is a classical statistical model to cluster the heterogeneous population into homogeneous sub-populations. However, for the highly heterogeneous population with multiple components, its parameter estimation and clustering results may be ambiguous due to the dependence of the EM algorithm on the initial values. For sub-typing purposes, the finite mixture of regression models with concomitant variables is considered and a novel statistical method is proposed to identify the main components with large proportions in the mixture sequentially. Compared to existing typical statistical inferences, the new method not only requires no pre-specification on the number of components for model fitting, but also provides more reliable parameter estimation and clustering results. Simulation studies demonstrated the superiority of the proposed method. Real data analysis on the drug response prediction illustrated its reliability in the parameter estimation and capability to identify the important subgroup