Coretto, P;
Hennig, C;
(2017)
Consistency, Breakdown Robustness, and Algorithms for Robust Improper Maximum Likelihood Clustering.
Journal of Machine Learning Research
, 18
(142)
pp. 1-39.
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Abstract
The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo- likelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multivariate finite Gaussian mixture models. In this paper we treat existence, consistency, and breakdown theory for the RIMLE comprehensively. RIMLE's existence is proved under non-smooth covariance matrix constraints. It is shown that these can be implemented via a computationally feasible Expectation-Conditional Maximization algorithm.
| Type: | Article |
|---|---|
| Title: | Consistency, Breakdown Robustness, and Algorithms for Robust Improper Maximum Likelihood Clustering |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.jmlr.org/papers/v18/16-382.html |
| Language: | English |
| Additional information: | Copyright © 2017 Pietro Coretto and Christian Hennig. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v18/16-382.html. |
| Keywords: | Robustness, Improper density, Mixture models, Model-based clustering, Maximum likelihood, ECM-algorithm |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10027537 |
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