BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Inference in generative models using the Wasserstein distance - Ch ristian Robert (CNRS & Université Paris-Dauphine ) DTSTART:20170707T104500Z DTEND:20170707T113000Z UID:TALK73186@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:In purely generative models\, one can simulate data given para meters but not necessarily evaluate the likelihood. We use Wasserstein dis tances between empirical distributions of observed data and empirical dist ributions of synthetic data drawn from such models to estimate their param eters. Previous interest in the Wasserstein distance for statistical infer ence has been mainly theoretical\, due to computational limitations. Thank s to recent advances in numerical transport\, the computation of these dis tances has become feasible\, up to controllable approximation errors. We l everage these advances to propose point estimators and quasi-Bayesian dist ributions for parameter inference\, first for independent data. For depend ent data\, we extend the approach by using delay reconstruction and residu al reconstruction techniques. For large data sets\, we propose an alternat ive distance using the Hilbert space-filling curve\, which computation sca les as n log n where n is the size of the data. We pr ovide a theoretical study of the proposed estimators\, and adaptive Monte Carlo algorithms to approximate them. The approach is illustrated on four examples: a quantile g-and-k distribution\, a toggle switch model from sys tems biology\, a Lotka-Volterra model for plankton population sizes and a L\\'\;evy-driven stochastic volatility model.

[This is joi nt work with Espen Bernton (Har vard University)\, Pierre E. Jacob (Harvard Un iversity)\, Mathieu Gerber (University of Bri stol).]

LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR