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Séminaire du département Images et Signal du 17/05/2018 à 14h00

 

Application of Quasi-Monte Carlo to approximate Bayesian computation and variational inference

Intervenant : Alexander BUCHHOLZ, ENSAE

Lieu : Salle Chartreuse

 

Résumé :

Standard Monte Carlo (MC) methods approach the problem of integrating a function with respect to a random variable by independently sampling from the target space and calculating the empirical mean over the generated samples. 
Quasi Monte Carlo (QMC) or low discrepancy sequences tackle the same problem by generating deterministic sequences that cover the target space more evenly. If the target function is regular enough, this approach leads to a faster rate of convergence of the approximation error than its MC counterpart. We use this idea in the context of likelihood free inference, also called approximate Bayesian computation, that applies to models where one is able to simulate from the model but is not able to evaluate the likelihood of the model.
As a second application we study the benefits of QMC in the field of variational inference, a machine learning technique that is used for approximating posterior distributions by a family of tractable distributions.


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