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The MIT Statistics and Data Science Center hosts guest lecturers from around the world in this weekly seminar.
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Large girth approximate Steiner triple systems
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…
Find out more »Reducibility and Computational Lower Bounds for Some High-dimensional Statistics Problems
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…
Find out more »Bias Reduction and Asymptotic Efficiency in Estimation of Smooth Functionals of High-Dimensional Covariance
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…
Find out more »Model-X knockoffs for controlled variable selection in high dimensional nonlinear regression
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…
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 »Joint estimation of parameters in Ising Model
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…
Find out more »Alan Frieze
Carnegie Melon University
MIT Statistics and Data Science Center host guest lecturers from around the world in this weekly seminar.
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 »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 »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…
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