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Past Events › Stochastics and Statistics Seminar Series

The MIT Statistics and Data Science Center hosts guest lecturers from around the world in this weekly seminar.

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February 2019

TAP free energy, spin glasses, and variational inference

February 15, 2019 @ 11:00 am - 12:00 pm

Zhou Fan (Yale University)

E18-304

Abstract: We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as "Z2 synchronization". Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy. We prove that this identification…

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Medical Image Imputation

February 8, 2019 @ 11:00 am - 12:00 pm

Polina Golland (MIT CSAIL)

E18-304

Abstract: We present an algorithm for creating high resolution anatomically plausible images that are consistent with acquired clinical brain MRI scans with large inter-slice spacing. Although large databases of clinical images contain a wealth of information, medical acquisition constraints result in sparse scans that miss much of the anatomy. These characteristics often render computational analysis impractical as standard processing algorithms tend to fail when applied to such images. Our goal is to enable application of existing algorithms that were originally…

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Optimization of the Sherrington-Kirkpatrick Hamiltonian

February 1, 2019 @ 11:00 am - 12:00 pm

Andrea Montanari (Stanford University )

E18-304

Andrea Montanari Professor, Department of Electrical Engineering, Department of Statistics Stanford University This lecture is in conjunction with the LIDS Student Conference. Abstract: Let A be n × n symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing xT Ax over binary vectors with ±1 entries. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this…

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December 2018

Large girth approximate Steiner triple systems

December 14, 2018 @ 11:00 am - 12:00 pm

Lutz Warnke (Georgia Institute of Technology)

E18-304

Abstract: In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element vertex-set contains at least g-2 triples.) We answer this question, by showing existence of approximate Steiner triple systems with arbitrary high girth. More concretely, for any fixed \ell \ge 4 we show that a natural constrained random process typically produces a partial Steiner triple…

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

December 7, 2018 @ 11:00 am - 12:00 pm

Guy Bresler (MIT)

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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November 2018

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

November 30, 2018 @ 11:00 am - 12:00 pm

Vladimir Koltchinskii (Georgia Institute of Technology)

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 → 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 sufficiently…

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

November 16, 2018 @ 11:00 am - 12:00 pm

Lucas Janson (Harvard University )

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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Optimal hypothesis testing for stochastic block models with growing degrees

November 9, 2018 @ 11:00 am - 12:00 pm

Zongming Ma (University of Pennsylvania)

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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Joint estimation of parameters in Ising Model

November 2, 2018 @ 11:00 am - 12:00 pm

Sumit Mukherjee (Columbia University)

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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October 2018

Alan Frieze

October 26, 2018 @ 11:00 am - 12:00 pm

Carnegie Melon University

MIT Statistics and Data Science Center host guest lecturers from around the world in this weekly seminar.

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