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Stochastics and Statistics Seminar Joan Bruna, New York University

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Stochastics and Statistics Seminar Vitaly Feldman, Apple ML Research

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Stochastics and Statistics Seminar Mark Sellke, Harvard University

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Stochastics and Statistics Seminar Edward Kennedy, Carnegie Mellon University

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On Provably Learning Sparse High-Dimensional Functions

Joan Bruna, New York University
E18-304

Abstract: Neural Networks are hailed for their ability to discover useful low-dimensional 'features' out of complex high-dimensional data, yet such ability remains mostly hand-wavy. Over the recent years, the class of sparse (or 'multi-index') functions has emerged as a model with both practical motivations and a rich mathematical structure, enabling a quantitative theory of 'feature learning'. In this talk,…

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Efficient Algorithms for Locally Private Estimation with Optimal Accuracy Guarantees

Vitaly Feldman, Apple ML Research
E18-304

Abstract: Locally Differentially Private (LDP) reports are commonly used for collection of statistics and machine learning in the federated setting with an untrusted server. We study the efficiency of two basic tasks, frequency estimation and vector mean estimation, using LDP reports. Existing algorithms for these problems that achieve the lowest error are neither communication nor…

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Confinement of Unimodal Probability Distributions and an FKG-Gaussian Correlation Inequality

Mark Sellke, Harvard University
E18-304

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…

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Optimal nonparametric capture-recapture methods for estimating population size

Edward Kennedy, Carnegie Mellon University
E18-304

Abstract: Estimation of population size using incomplete lists has a long history across many biological and social sciences. For example, human rights groups often construct partial lists of victims of armed conflicts, to estimate the total number of victims. Earlier statistical methods for this setup often use parametric assumptions, or rely on suboptimal plug-in-type nonparametric estimators;…

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