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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 34

Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold

February 1, 2023

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Abstract:

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.

Published Date: 2020-06-02

Registration: ISSN 2374-3468 (Online) ISSN 2159-5399 (Print) ISBN 978-1-57735-835-0 (10 issue set)

Copyright: Published by AAAI Press, Palo Alto, California USA Copyright © 2020, Association for the Advancement of Artificial Intelligence All Rights Reserved

Authors

Shengxi Li

Imperial College London


Zeyang Yu

Imperial College London


Min Xiang

Imperial College London


Danilo Mandic

Imperial College London


DOI:

10.1609/aaai.v34i04.5897


Topics: AAAI

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HOW TO CITE:

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold Proceedings of the AAAI Conference on Artificial Intelligence, 34 (2020) 4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold AAAI 2020, 4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic (2020). Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold. Proceedings of the AAAI Conference on Artificial Intelligence, 34, 4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold. Proceedings of the AAAI Conference on Artificial Intelligence, 34 2020 p.4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. 2020. Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold. "Proceedings of the AAAI Conference on Artificial Intelligence, 34". 4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. (2020) "Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold", Proceedings of the AAAI Conference on Artificial Intelligence, 34, p.4658-4666

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic, "Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold", AAAI, p.4658-4666, 2020.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. "Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold". Proceedings of the AAAI Conference on Artificial Intelligence, 34, 2020, p.4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. "Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold". Proceedings of the AAAI Conference on Artificial Intelligence, 34, (2020): 4658-4666.

Shengxi Li||Zeyang Yu||Min Xiang||Danilo Mandic. Solving General Elliptical Mixture Models through an Approximate Wasserstein Manifold. AAAI[Internet]. 2020[cited 2023]; 4658-4666.


ISSN: 2374-3468


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