Convergence and efficiency of adaptive importance sampling techniques with partial biasing

Gersende Fort 1 Benjamin Jourdain 2, 3 Tony Lelievre 4, 2 Gabriel Stoltz 2, 4
3 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
4 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which is an adaptive importance technique useful to sample multimodal target distributions. The importance function is based on the weights of disjoint sets which form a partition of the space. In the context of computational statistical physics, the logarithm of these weights is, up to a multiplicative constant, the free energy, and the discrete valued function defining the partition is called the reaction coordinate. The algorithm is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets and (ii) the target distribution is biased using only a fraction of the free energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. The algorithm can also be seen as a generalization of well-tempered metadynamics. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01389996
Contributeur : Benjamin Jourdain <>
Soumis le : lundi 31 octobre 2016 - 10:05:51
Dernière modification le : samedi 18 février 2017 - 01:17:35

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  • HAL Id : hal-01389996, version 1
  • ARXIV : 1610.09194

Citation

Gersende Fort, Benjamin Jourdain, Tony Lelievre, Gabriel Stoltz. Convergence and efficiency of adaptive importance sampling techniques with partial biasing. 2016. 〈hal-01389996〉

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