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Stochastics and Statistics Seminar
Confinement of Unimodal Probability Distributions and an FKG-Gaussian Correlation Inequality
March 22 @ 11:00 am - 12:00 pm
Mark Sellke, Harvard University
E18-304
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Abstract:
While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g. variance upper bounds) for high-dimensional unimodal distributions which are not log-concave, based on an extension of Royen’s celebrated Gaussian correlation inequality. We will see how it yields new localization results for Ginzberg-Landau random surfaces, a well-studied family of continuous-variable graphical models, with very general monotone potentials that need not be convex.
While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g. variance upper bounds) for high-dimensional unimodal distributions which are not log-concave, based on an extension of Royen’s celebrated Gaussian correlation inequality. We will see how it yields new localization results for Ginzberg-Landau random surfaces, a well-studied family of continuous-variable graphical models, with very general monotone potentials that need not be convex.
Bio:
Mark Sellke is an Assistant Professor of Statistics at Harvard. His research interests are in probability, optimization, and learning theory, with a particular focus on spin glasses. Mark completed his PhD at Stanford and his undergraduate degree at MIT, both in mathematics. His work has been recognized by best paper awards at SODA and NeurIPS.
Mark Sellke is an Assistant Professor of Statistics at Harvard. His research interests are in probability, optimization, and learning theory, with a particular focus on spin glasses. Mark completed his PhD at Stanford and his undergraduate degree at MIT, both in mathematics. His work has been recognized by best paper awards at SODA and NeurIPS.
