Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering

Simon Lacoste-Julien 1, 2, 3 Fredrik Lindsten 4 Francis Bach 1, 2, 3
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure to obtain adaptive quadrature rules for integrals of functions in a reproducing kernel Hilbert space (RKHS) with a potentially faster rate of convergence than Monte Carlo integration (and "kernel herding" was shown to be a special case of this procedure). In this paper, we propose to replace the random sampling step in a particle filter by Frank-Wolfe optimization. By optimizing the position of the particles, we can obtain better accuracy than random or quasi-Monte Carlo sampling. In applications where the evaluation of the emission probabilities is expensive (such as in robot localization), the additional computational cost to generate the particles through optimization can be justified. Experiments on standard synthetic examples as well as on a robot localization task indicate indeed an improvement of accuracy over random and quasi-Monte Carlo sampling.
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https://hal.archives-ouvertes.fr/hal-01099197
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Submitted on : Monday, February 9, 2015 - 9:06:11 PM
Last modification on : Thursday, February 7, 2019 - 3:49:22 PM
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  • HAL Id : hal-01099197, version 2
  • ARXIV : 1501.02056

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Simon Lacoste-Julien, Fredrik Lindsten, Francis Bach. Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering. 18th International Conference on Artificial Intelligence and Statistics (AISTATS), May 2015, San Diego, United States. ⟨hal-01099197v2⟩

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