4 research outputs found
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