Bayes in Grenoble: Youssef Marzouk

on the March 26, 2019

March, 26th at 2:00 pm
Youssef Marzouk (MIT) will talk about "Nonlinear filtering and smoothing with transport maps". The event will take place on March, 26 at 2:00 pm at Imag building.
Bayes in Grenoble is a new reading group on Bayesian statistical methods. The purpose of this group is to gather the Grenoble Bayesian community on a monthly basis around noteworthy papers. Those can equally focus on theory, methods, learning, applications, computations, etc, and can be seminal papers as well as recent preprints, as soon as they relate to Bayes.

The sessions last two hours: the presentation is followed by an informal moment where participants will enjoy cocktails and snacks offered by the Grenoble Alpes Data Institute.

The reading group is organised by Julyan Arbel and Florence Forbes. Feel free to contact them if you wish to attend/be added to the mailing list and/or give a talk.

React on social media: #BIGseminar

26 March 2019, Youssef Marzouk (MIT)

Nonlinear filtering and smoothing with transport maps


We consider the Bayesian filtering problem for high dimensional non-Gaussian state-space models with challenging nonlinear dynamics, and sparse observations in space and time. While the ensemble Kalman filter (EnKF) yields robust ensemble approximations of the filtering distribution, it is limited by linear forecast-to-analysis transformations. To generalize the EnKF, we propose a methodology that transforms the non-Gaussian forecast ensemble at each assimilation step into samples from the current filtering distribution via a sequence of local nonlinear couplings. These couplings are based on transport maps that can be computed quickly using convex optimization, and that can be enriched in complexity to reduce the intrinsic bias of the EnKF. We discuss the low-dimensional structure inherited by the transport maps from the filtering problem, including decay of correlations, conditional independence, and local likelihoods. We then exploit this structure to regularize the estimation of the maps in high dimensions and with a limited ensemble size.

We also present variational methods---again based on transport maps---for filtering, smoothing, and sequential parameter estimation in non-Gaussian state-space models. These methods rely on results linking the Markov properties of a target measure to the existence of low-dimensional couplings, induced by transport maps that are decomposable. The resulting algorithms can be understood as a generalization, to the non-Gaussian case, of the square-root Rauch--Tung--Striebel Gaussian smoother.

This is joint work with Ricardo Baptista, Daniele Bigoni, and Alessio Spantini.

Published on March 19, 2019

Practical informations


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