1. Gradient-based adaptive importance samplers
- Author
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Elvira, Víctor, Chouzenoux, Emilie, Akyildiz, Ömer Deniz, Martino, Luca, School of Mathematics - University of Edinburgh, University of Edinburgh, OPtimisation Imagerie et Santé (OPIS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de vision numérique (CVN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-CentraleSupélec-Université Paris-Saclay, Centre de vision numérique (CVN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay, Imperial College London, Universidad Rey Juan Carlos [Madrid] (URJC), ANR-17-CE40-0031,PISCES,Méthodes d'échantillonnage d'importance adaptatives pour l'inférence Bayésienne dans les systèmes complexes(2017), European Project: ERC-2019-STG-850925,MAJORIS(2020), Chouzenoux, Emilie, Méthodes d'échantillonnage d'importance adaptatives pour l'inférence Bayésienne dans les systèmes complexes - - PISCES2017 - ANR-17-CE40-0031 - AAPG2017 - VALID, ERC-2019-STG-850925 - MAJORIS - ERC-2019-STG-850925 - INCOMING, and Inria Saclay - Île de France
- Subjects
FOS: Computer and information sciences ,Poisson field ,Bayesian inference ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) ,Statistics - Computation ,Adaptive importance sampling ,FOS: Mathematics ,Gaussian mixture ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,Monte Carlo ,[STAT.ME]Statistics [stat]/Methodology [stat.ME] ,Computation (stat.CO) ,Langevin adaptation ,[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing - Abstract
International audience; Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability distribution. The performance of IS heavily depends on the appropriate selection of the proposal distributions where the samples are simulated from. In this paper, we propose an adaptive importance sampler, called GRAMIS, that iteratively improves the set of proposals. The algorithm exploits geometric information of the target to adapt the location and scale parameters of those proposals. Moreover, in order to allow for a cooperative adaptation, a repulsion term is introduced that favors a coordinated exploration of the state space. This translates into a more diverse exploration and a better approximation of the target via the mixture of proposals. Moreover, we provide a theoretical justification of the repulsion term. We show the good performance of GRAMIS in two problems where the target has a challenging shape and cannot be easily approximated by a standard uni-modal proposal.
- Published
- 2023
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