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 multi-variate 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.

Coretto, P., Hennig, C. (2017). Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering. JOURNAL OF MACHINE LEARNING RESEARCH, 18, 1-39.

Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering

Hennig, Christian
2017

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 multi-variate 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.
2017
Coretto, P., Hennig, C. (2017). Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering. JOURNAL OF MACHINE LEARNING RESEARCH, 18, 1-39.
Coretto, Pietro; Hennig, Christian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/677283
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