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February 2019

Capacity lower bound for the Ising perceptron

Nike Sun (MIT)

February 22 @ 11:00 am - 12:00 pm

Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results. This is a joint work with Jian Ding. Biography: Nike Sun is a…

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March 2019

Why Aren’t Network Statistics Accompanied By Uncertainty Statements?

Eric Kolaczyk (Boston University)

March 1 @ 11:00 am - 12:00 pm

Abstract: Over 500K scientific articles have been published since 1999 with the word “network” in the title. And the vast majority of these report network summary statistics of one type or another. However, these numbers are rarely accompanied by any quantification of uncertainty. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Perhaps surprisingly, there is little in the way of…

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Univariate total variation denoising, trend filtering and multivariate Hardy-Krause variation denoising

Aditya Guntuboyina (UC Berkley)

March 8 @ 11:00 am - 12:00 pm

Abstract: Total variation denoising (TVD) is a popular technique for nonparametric function estimation. I will first present a theoretical optimality result for univariate TVD for estimating piecewise constant functions. I will then present related results for various extensions of univariate TVD including adaptive risk bounds for higher-order TVD (also known as trend filtering) as well as a multivariate extension via the Hardy-Krause Variation which avoids the curse of dimensionality to some extent. I will also mention connections to shape restricted…

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Subvector Inference in Partially Identified Models with Many Moment Inequalities

Alex Belloni (Duke University)

March 15 @ 11:00 am - 12:00 pm

Abstract: In this work we consider bootstrap-based inference methods for functions of the parameter vector in the presence of many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. In particular this covers the case of subvector inference, such as the inference on a single component associated with a treatment/policy variable of interest. We consider a min-max of (centered and non-centered) Studentized statistics and study the properties of the…

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Optimization of random polynomials on the sphere in the full-RSB regime

Eliran Subag (New York University)

March 22 @ 11:00 am - 12:00 pm

Abstract: The talk will focus on optimization on the high-dimensional sphere when the objective function is a linear combination of homogeneous polynomials with standard Gaussian coefficients. Such random processes are called spherical spin glasses in physics, and have been extensively studied since the 80s. I will describe certain geometric properties of spherical spin glasses unique to the full-RSB case, and explain how they can be used to design a polynomial time algorithm that finds points within small multiplicative error from…

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April 2019

Exponential line-crossing inequalities

Aaditya Ramdas (Carnegie Mellon University)

April 12 @ 11:00 am - 12:00 pm

Abstract: This talk will present a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities in this way. We will illustrate this point by presenting a single assumption and a single theorem that together strengthen many tail bounds for martingales, including classical inequalities (1960-80) by Bernstein, Bennett, Hoeffding, and Freedman; contemporary inequalities (1980-2000) by Shorack and Wellner,…

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Logistic Regression: The Importance of Being Improper

Dylan Foster (MIT Institute for Foundations of Data Science)

April 19 @ 11:00 am - 12:00 pm

Abstract: Logistic regression is a fundamental task in machine learning and statistics. For the simple case of linear models, Hazan et al. (2014) showed that any logistic regression algorithm that estimates model weights from samples must exhibit exponential dependence on the weight magnitude. As an alternative, we explore a counterintuitive technique called improper learning, whereby one estimates a linear model by fitting a non-linear model. Past success stories for improper learning have focused on cases where it can improve computational…

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Robust Estimation: Optimal Rates, Computation and Adaptation

Chao Gao (University of Chicago)

April 26 @ 11:00 am - 12:00 pm

Abstract: Chao Gao will discuss the problem of statistical estimation with contaminated data. In the first part of the talk, I will discuss depth-based approaches that achieve minimax rates in various problems. In general, the minimax rate of a given problem with contamination consists of two terms: the statistical complexity without contamination, and the contamination effect in the form of modulus of continuity. In the second part of the talk, I will discuss computational challenges of these depth-based estimators. An…

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May 2019

Stochastics and Statistics Seminar: Optimal Adaptivity of Signed-Polygon Statistics for Network Testing (Tracy Ke, Harvard University)

Tracy Ke (Harvard University)

May 3 @ 11:00 am - 12:00 pm

Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a tractable null distribution, and (d) adapt automatically to different levels of sparsity, and achieve the optimal detection boundary. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fix m ≥ 3. For each m-gon…

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Counting and sampling at low temperatures

Will Perkins (University of Illinois at Chicago)

May 10 @ 11:00 am - 12:00 pm

Abstract: We consider the problem of efficient sampling from the hard-core and Potts models from statistical physics. On certain families of graphs, phase transitions in the underlying physics model are linked to changes in the performance of some sampling algorithms, including Markov chains. We develop new sampling and counting algorithms that exploit the phase transition phenomenon and work efficiently on lattices (and bipartite expander graphs) at sufficiently low temperatures in the phase coexistence regime. Our algorithms are based on Pirogov-Sinai…

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