Monday, April 12, 2021
04/12/2021 - 10:00am
Abstract: Many practical Bayesian inference problems fall into the “likelihood-free” setting, where evaluations of the likelihood function or prior density are unavailable or intractable. I will discuss how transportation of measure can solve such problems, by constructing maps that push prior samples, or samples from a joint parameter-data prior, to the desired conditional distribution. These methods have broad utility for inference in stochastic and generative models, as well as for data assimilation problems motivated by geophysical applications. Key issues in this construction center on: (1) the estimation of these transport maps from samples; and (2) parameterizations of monotone maps. I will discuss developments on both fronts, focusing on a composition-of-maps approach that improves finite-sample performance.
As an example, I will present a new approach to nonlinear filtering in dynamical systems which uses sparse triangular transport maps to produce robust approximations of the filtering distribution in high dimensions. The approach can be understood as the natural generalization of the ensemble Kalman filter (EnKF) to nonlinear updates, and can reduce the intrinsic bias of the EnKF at a marginal increase in computational cost.
This is joint work with Ricardo Baptista, Alessio Spantini, and Olivier Zahm.
Contact email@example.com for information.
Zoom Meeting ID: 97670014308
04/12/2021 - 10:15am
For some non-compact semisimple Lie groups G there are connected
04/12/2021 - 4:30pm
The commuting scheme has always been of great interest in invariant theory but it was only recent that it appears as a primordial object in the study of the Hitchin fibration for higher dimensional varieties. I will explain how the invariant theory for the commuting scheme, in particular the Chevalley restriction theorem for the commuting scheme, was used in the study of Hitchin fibration and the proof of the Chevalley restriction theorem in the case of symplectic Lie algebras. The talk is based on joint work with Ngo Bao Chau.
https://yale.zoom.us/j/92811265790 (Password is the same as last semester)