Duality results and proximal solutions of the Huber M-estimator problem |
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Authors: | C. Michelot M. L. Bougeard |
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Affiliation: | (1) CERMSEM Université de Paris I, 90 rue de Tolbiac, 75634 Paris Cedex 13, France;(2) Université de Bourgogne, BP 138, 21004 Dijon Cedex, France;(3) URA 1125, CNRS, Observatoire de Paris, 61 av. Observatoire, 75014 Paris, France |
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Abstract: | We investigate the interest of solving the Huber M-estimator problem by a proximal approach combined with duality theory. Three different duality schemes are developed. The first one which only deals with estimator determination yields useful information on the geometrical structure of the set of optimal solutions. The second scheme links together estimator determination and outliers detection while the third one only focuses on outliers separation. We show that these three duality schemes can be solved by the partial inverse method, i.e., a special instance of the basic proximal point algorithm, which leads to very simple updating rules. This method which is always globally convergent enjoys nice stability properties and permits parallel computations. |
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Keywords: | Robustness Huber M-estimator Outliers identification Duality Proximal algorithm Partial inverse method |
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