## Past Events › Stochastics and Statistics Seminar

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## Reverse hypercontractivity beats measure concentration for information theoretic converses

Jingbo Liu (MIT)

Abstract: Concentration of measure refers to a collection of tools and results from analysis and probability theory that have been used in many areas of pure and applied mathematics. Arguably, the first data science application of measure concentration (under the name ‘‘blowing-up lemma’’) is the proof of strong converses in multiuser information theory by Ahlswede, G'acs and K"orner in 1976. Since then, measure concentration has found applications in many other information theoretic problems, most notably the converse (impossibility) results in…

Find out more »## Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs

Tselil Schramm (Harvard University)

Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known. Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng. Biography: Tselil Schramm is a postdoc in theoretical…

Find out more »## Locally private estimation, learning, inference, and optimality

John Duchi (Stanford University)

Abstract: In this talk, we investigate statistical learning and estimation under local privacy constraints, where data providers do not trust the collector of the data and so privatize their data before it is even collected. We identify fundamental tradeoffs between statistical utility and privacy in such local models of privacy, providing instance-specific bounds for private estimation and learning problems by developing local minimax risks. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to…

Find out more »## Algorithmic thresholds for tensor principle component analysis

Aukosh Jagannath (Harvard University)

Abstract: Consider the problem of recovering a rank 1 tensor of order k that has been subject to Gaussian noise. The log-likelihood for this problem is highly non-convex. It is information theoretically possible to recover the tensor with a finite number of samples via maximum likelihood estimation, however, it is expected that one needs a polynomially diverging number of samples to efficiently recover it. What is the cause of this large statistical–to–algorithmic gap? To study this question, we investigate the…

Find out more »## On the cover time of two classes of graph

Alan Frieze (Carnegie Mellon University)

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…

Find out more »## Joint estimation of parameters in Ising Model

Sumit Mukherjee (Columbia University)

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…

Find out more »## Optimal hypothesis testing for stochastic block models with growing degrees

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…

Find out more »## Model-X knockoffs for controlled variable selection in high dimensional nonlinear regression

Lucas Janson (Harvard University)

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…

Find out more »## Bias Reduction and Asymptotic Eﬃciency in Estimation of Smooth Functionals of High-Dimensional Covariance

Vladimir Koltchinskii (Georgia Institute of Technology)

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…

Find out more »## Reducibility and Computational Lower Bounds for Some High-dimensional Statistics Problems

Guy Bresler (MIT)

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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