[IDA ML Seminar] IDA Machine Learning Seminar 21/4 - Rémi Bardenet

[Fredrik Lindsten]

Welcome to the IDA Machine Learning Seminar on Wednesday, April 21, 
15:15 (Swedish time)

Rémi Bardenet, CNRS & CRIStAL, Université de Lille, France
http://rbardenet.github.io/

Monte Carlo integration with repulsive point processes
Abstract: Monte Carlo integration is the workhorse of Bayesian 
inference, but the mean square error of Monte Carlo estimators decreases 
slowly, typically as 1/N, where N is the number of integrand 
evaluations. This becomes a bottleneck in Bayesian applications where 
evaluating the integrand can take tens of seconds, like in the life 
sciences, where evaluating the likelihood often requires solving a large 
system of differential equations. I will present two approaches to 
faster Monte Carlo rates using interacting particle systems. First, I 
will show how results from random matrix theory lead to a stochastic 
version of Gaussian quadrature in any dimension d, with mean square 
error decreasing as 1/N^{1+1/d}. This quadrature is based on 
determinantal point processes, which can be argued to be the kernel 
machine of point processes. Second, I will show how to further take this 
error rate down assuming the integrand is smooth. In particular, I will 
give a tight error bound when the integrand belongs to any arbitrary 
reproducing kernel Hilbert space, using a mixture of determinantal point 
processes tailored to that space. This mixture is reminiscent of volume 
sampling, a randomized experimental design used in linear regression.

Joint work with Adrien Hardy, Ayoub Belhadji, Pierre Chainais

Zoom link: https://liu-se.zoom.us/j/69011766298
Passcode: 742124



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The list of future seminars in the series is available at 
http://www.ida.liu.se/research/machinelearning/seminars/.

Welcome!​
IDA Machine Learning Group
Linköping University
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