The CFM – Imperial Institute of Quantitative Finance is pleased to announce a series of Distinguished Lectures by Pierre Del Moral (INRIA, France) on Mean Field Particle Samplers in Statistical Learning and Rare Event Analysis.
In the last three decades, there has been a dramatic increase in the use of mean field particle sampling methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. The particle simulation techniques they suggest are also called resampled and diffusion Monte Carlo methods in quantum physics, genetic and evolutionary type algorithms in computer sciences, as well as Sequential Monte Carlo methods in Bayesian statistics, and particle filters in advanced signal processing. These particle methodologies are used to approximate a flow of probability measures with an increasing level of complexity. This class of probabilistic models includes conditional distributions of signals with respect to noisy and partial observations, non-absorption probabilities in Feynman–Kac–Schrödinger type models, Boltzmann–Gibbs measures, calibration and propagation of uncertainty probabilities, as well as conditional distributions of stochastic processes in critical regimes, including quasi-invariant measures and ground state computations.
This series of lectures present an introduction to the stochastic modeling and theoretical analysis of these sophisticated probabilistic models. We shall discuss the origins and mathematical foundations of these particle stochastic methods, and applications in rare event analysis, signal processing, mathematical finance and Bayesian statistical inference. We illustrate these methods through several applications: random walk confinements, particle absorption models, nonlinear filtering, stochastic optimization, combinatorial counting and directed polymer models.
Lecture 4 – SOME THEORETICAL ASPECTS
(Tuesday November 8, 09:30-11:00, CDT Lecture Room 1)
The fourth and last of these lectures is concerned with the mathematical foundations and the theoretical aspects of the particle samplers discussed in the first lectures. We discuss some key stochastic analysis techniques including the analysis of the stability properties of nonlinear Feynman-Kac semigroups, and local linearization and perturbation analysis of mean field particle models.
Further information can be found here.
Due to limited seats, registration is compulsory – please register by emailing Ms Marta Guzzon at m.guzzon@imperial.ac.uk.