# Normalizing constants of log-concave densities

Abstract : We derive explicit bounds for the computation of normalizing constants Z for log-concave densities $π = e −U /Z$ w.r.t. the Lebesgue measure on $R d$. Our approach relies on a Gaussian annealing combined with recent and precise bounds on the Unadjusted Langevin Algorithm [13]. Polynomial bounds in the dimension d are obtained with an exponent that depends on the assumptions made on U. The algorithm also provides a theoretically grounded choice of the annealing sequence of variances. A numerical experiment supports our findings. Results of independent interest on the mean squared error of the empirical average of locally Lipschitz functions are established.
Keywords :
Type de document :
Pré-publication, Document de travail
2017
Domaine :
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Littérature citée [43 références]

https://hal.inria.fr/hal-01648666
Contributeur : Nicolas Brosse <>
Soumis le : lundi 27 novembre 2017 - 23:25:23
Dernière modification le : jeudi 11 janvier 2018 - 06:23:39

### Identifiants

• HAL Id : hal-01648666, version 1

### Citation

Nicolas Brosse, Alain Durmus, Eric Moulines. Normalizing constants of log-concave densities. 2017. 〈hal-01648666〉

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