Monte Carlo with determinantal point processes (Talk)
In this talk, we show that using repulsive random variables, it is possible to build Monte Carlo methods that converge faster than vanilla Monte Carlo. More precisely, we build estimators of integrals, the variance of which decreases as $N^{-1-1/d}$, where $N$ is the number of integrand evaluations, and $d$ is the ambient dimension. To do so, we propose stochastic numerical quadratures involving determinantal point processes (DPPs) associated to multivariate orthogonal polynomials. The proposed method can be seen as a stochastic version of Gauss' quadrature, where samples from a determinantal point process replace zeros of orthogonal polynomials. Furthermore, integration with DPPs is close in spirit to randomized quasi-Monte Carlo methods, leveraging repulsive point processes to ensure low discrepancy samples. The talk is based on the following preprint https://arxiv.org/abs/1605.00361
Biography: Rémi Bardenet is a CNRS junior permanent researcher at University of Lille (France) working on computational statistics. He received his M.Sc. degree in Mathematics, Computer Vision, and Machine Learning from Ecole Normale Supérieure, Cachan (France) in 2009 and his Ph.D. in Computer Science from Université Paris-Sud XI, Orsay (France) in 2012. He subsequently spent two years as a postdoctoral fellow at the Department of Statistics, University of Oxford until 2015. His research interests include probabilistic modelling and inference, Monte Carlo methods, and applications of these to machine learning, particle physics and computational biology.
Details
- 02 November 2016 • 15:00 - 16:00
- AGBS Seminar room (Spemannstr. 38)
- Intelligent Systems