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Poster
Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting
Rebecca Morrison · Ricardo Baptista · Youssef Marzouk

Mon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #180 #None

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another.

Author Information

Rebecca Morrison (Massachusetts Institute of Technology)
Ricardo Baptista (MIT)
Youssef Marzouk (Massachusetts Institute of Technology)

Youssef Marzouk is a Professor in the Department of Aeronautics and Astronautics at MIT, and co-director of the MIT Center for Computational Science & Engineering. He is also a core member of MIT's Statistics and Data Science Center and director of the MIT Aerospace Computational Design Laboratory. His research interests lie at the intersection of computation and statistical inference with physical modeling. He develops new methodologies for uncertainty quantification, Bayesian modeling and computation, data assimilation, experimental design, and machine learning in complex physical systems. His methodological work is motivated by a wide variety of engineering, environmental, and geophysics applications. He received his SB, SM, and PhD degrees from MIT and spent four years at Sandia National Laboratories before joining the MIT faculty in 2009. He is a recipient of the Hertz Foundation Doctoral Thesis Prize, the Sandia Laboratories Truman Fellowship, the US Department of Energy Early Career Research Award, and the Junior Bose Award for Teaching Excellence from the MIT School of Engineering. He is an Associate Fellow of the AIAA and currently serves on the editorial boards of the SIAM Journal on Scientific Computing, the SIAM/ASA Journal on Uncertainty Quantification, and several other journals. He is also an avid coffee drinker and occasional classical pianist.

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