Wednesday, November 16, 2016 - 4:30pm
Event Calendar Category
LIDS & Stats Tea
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We describe a nonparametric variational inference method that approximates an intractable target measure as the pushforward of a tractable distribution (e.g., a Gaussian) through a transport map, and that can approximate arbitrary probabilistic interactions, well beyond the usual mean-field approximations. We then show how such transport maps can be decomposed---i.e., factorized into the composition of finitely many low-dimensional maps---and establish a connection between decomposable transport maps and the sparsification of Markov networks. Finally, we use the notion of decomposable transports to derive new deterministic online algorithms for Bayesian filtering and smoothing in nonlinear/non-Gaussian state-space models with static parameters.
This is a joint work with Daniele Bigoni and Youssef Marzouk.
My current research addresses the methodology of high-dimensional Bayesian inference for a broad range of applications including nonlinear filtering and smoothing. In particular, I focus on the intersection of measure transport, nonparametric variational inference, optimal low-rank approximations and Monte Carlo methods. My background and general interests lie at the interface of statistics, probability, differential geometry, numerical analysis, and optimization. I grew up in Italy and I graduated in Aerospace Engineering from Politecnico di Milano in July, 2011. In my free time I enjoy sailing and jogging. I also hold a private pilot license.