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October 2018

Topics in Information and Inference Seminar

Abbas El Gamal (Stanford University)

October 25 @ 4:00 pm - 5:00 pm

This seminar consists of a series of lectures each followed by a period of informal discussion and social. The topics are at the nexus of information theory, inference, causality, estimation, and non-convex optimization. The lectures are intended to be tutorial in nature with the goal of learning about interesting and exciting topics rather than merely hearing about the most recent results. The topics are driven by the interests of the speakers, and with the exception of the two lectures on…

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On the cover time of two classes of graph

Alan Frieze (Carnegie Mellon University)

October 26 @ 11:00 am - 12:00 pm
E18-304

Abstract: Dense Graphs: We consider abritrary graphs G with n vertices and minimum degree at least n. where δ > 0 is constant. If the conductance of G is sufficiently large then we obtain an asymptotic expression for the cover time CG of G as the solution to some explicit transcendental equation. Failing this, if the mixing time of a random walk on G is of a lesser magnitude than the cover time, then we can obtain an asymptotic deterministic…

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November 2018

Topics in Information and Inference Seminar

Abbas El Gamal (Stanford University)

November 1 @ 4:00 pm - 5:00 pm

*This lecture is the second of two. The first lecture was given Thursday, October 25th. Title: Randomness and Information I and II Abstract: Exact or approximate generation of random variables with prescribed statistics from a given randomness source has many important applications, including random number generation from physical sources, Monte Carlo simulations, and randomized algorithms, e.g., for cryptography, optimization, and machine learning. It is also closely related to several fundamental questions in information theory, CS theory, and quantum information. The…

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Joint estimation of parameters in Ising Model

Sumit Mukherjee (Columbia University)

November 2 @ 11:00 am - 12:00 pm
E18-304

Abstract: Inference in the framework of Ising models has received significant attention in Statistics and Machine Learning in recent years. In this talk we study joint estimation of the inverse temperature parameter β, and the magnetization parameter B, given one realization from the Ising model, under the assumption that the underlying graph of the Ising model is completely specified. We show that if the graph is either irregular or sparse, then both the parameters can be estimated at rate n−1/2…

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Topics in Information and Inference Seminar

Suvrit Sra (MIT)

November 8 @ 4:00 pm - 5:00 pm
32-D677

This seminar consists of a series of lectures each followed by a period of informal discussion and social. The topics are at the nexus of information theory, inference, causality, estimation, and non-convex optimization. The lectures are intended to be tutorial in nature with the goal of learning about interesting and exciting topics rather than merely hearing about the most recent results. The topics are driven by the interests of the speakers, and with the exception of the two lectures on…

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Optimal hypothesis testing for stochastic block models with growing degrees

Zongming Ma (University of Pennsylvania)

November 9 @ 11:00 am - 12:00 pm
E18-304

Abstract: In this talk, we discuss optimal hypothesis testing for distinguishing a stochastic block model from an Erdos--Renyi random graph when the average degree grows to infinity with the graph size. We show that linear spectral statistics based on Chebyshev polynomials of the adjacency matrix can approximate signed cycles of growing lengths when the graph is sufficiently dense. The signed cycles have been shown by Banerjee (2018) to determine the likelihood ratio statistic asymptotically. In this way one achieves sharp…

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Topics in Information and Inference Seminar

Devavrat Shah (MIT)

November 15 @ 4:00 pm - 5:00 pm
32-D677

This seminar consists of a series of lectures each followed by a period of informal discussion and social. The topics are at the nexus of information theory, inference, causality, estimation, and non-convex optimization. The lectures are intended to be tutorial in nature with the goal of learning about interesting and exciting topics rather than merely hearing about the most recent results. The topics are driven by the interests of the speakers, and with the exception of the two lectures on…

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Model-X knockoffs for controlled variable selection in high dimensional nonlinear regression

Lucas Janson (Harvard University)

November 16 @ 11:00 am - 12:00 pm
E18-304

Abstract: Many contemporary large-scale applications, from genomics to advertising, involve linking a response of interest to a large set of potential explanatory variables in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively select important variables while controlling the fraction of false discoveries, even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new…

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Bias Reduction and Asymptotic Efficiency in Estimation of Smooth Functionals of High-Dimensional Covariance

Vladimir Koltchinskii (Georgia Institute of Technology)

November 30 @ 11:00 am - 12:00 pm
E18-304

Abstract: We discuss a recent approach to bias reduction in a problem of estimation of smooth functionals of high-dimensional parameters of statistical models. In particular, this approach has been developed in the case of estimation of functionals of covariance operator Σ : Rd d → Rd of the form f(Σ), B based on n i.i.d. observations X1, . . . , Xn sampled from the normal distribution with mean zero and covariance Σ, f : R → R being a…

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December 2018

Reducibility and Computational Lower Bounds for Some High-dimensional Statistics Problems

Guy Bresler (MIT)

December 7 @ 11:00 am - 12:00 pm
E18-304

Abstract: The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far exceeds what is needed for inefficient algorithms that search over all possible structures. A line of work initiated by Berthet and Rigollet in 2013 has aimed to explain these gaps by reducing from conjecturally hard problems in computer science. However, the delicate nature of average-case reductions has…

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