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

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Sampling rare events in Earth and planetary science

Jonathan Weare (New York University)
E18-304

Abstract: This talk will cover recent work in our group developing and applying algorithms to simulate rare events in atmospheric science and other areas. I will review a rare event simulation scheme that biases model simulations toward the rare event of interest by preferentially duplicating simulations making progress toward the event and removing others. I will describe applications of this approach to rapid intensification of tropical cyclones and instability of Mercury's orbit with an emphasis on the elements of algorithm…

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Beyond UCB: statistical complexity and optimal algorithm for non-linear ridge bandits

Yanjun Han (MIT)
E18-304

Abstract: Many existing literature on bandits and reinforcement learning assume a linear reward/value function, but what happens if the reward is non-linear? Two curious phenomena arise for non-linear bandits: first, in addition to the "learning phase" with a standard \Theta(\sqrt(T)) regret, there is an "initialization phase" with a fixed cost determined by the reward function; second, achieving the smallest cost of the initialization phase requires new learning algorithms other than traditional ones such as UCB. For a special family of…

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Short Stories about Data and Sports

Anette "Peko" Hosoi (MIT)
E18-304

ABSTRACT Recent advances in data collection have made sports an attractive testing ground for new analyses and algorithms, and a fascinating controlled microcosm in which to explore social interactions. In this talk I will describe two studies in this arena: one related to public health and the pandemic and one related to decision-making in basketball.  In the first, I will discuss what can be learned from the natural experiments that were (fortuitously) run in America football stadiums. During the 2020…

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Regularized modified log-Sobolev inequalities, and comparison of Markov chains

Konstantin Tikhomirov (Georgia Institute of Technology)
E18-304

Abstract: In this work, we develop a comparison procedure for the Modified log-Sobolev Inequality (MLSI) constants of two reversible Markov chains on a finite state space. As an application, we provide a sharp estimate of the MLSI constant of the switch chain on the set of simple bipartite regular graphs of size n with a fixed degree d. Our estimate implies that the total variation mixing time of the switch chain is of order O(n log(n)). The result is optimal up to a multiple…

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Efficient derivative-free Bayesian inference for large-scale inverse problems

Jiaoyang Huang (University of Pennsylvania)
E18-304

Abstract: We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for the repeated evaluations of an expensive forward model, which is often given as a black box or is impractical to differentiate. In this talk I will propose a new derivative-free algorithm Unscented Kalman Inversion, which utilizes the ideas from Kalman filter, to efficiently solve these inverse problems. First, I will explain some basics about Variational Inference under general metric tensors. In particular, under the…

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Maximum likelihood for high-noise group orbit estimation and cryo-EM

Zhou Fan (Yale University)
E18-304

Abstract: Motivated by applications to single-particle cryo-electron microscopy, we study a problem of group orbit estimation where samples of an unknown signal are observed under uniform random rotations from a rotational group. In high-noise settings, we show that geometric properties of the log-likelihood function are closely related to algebraic properties of the invariant algebra of the group action. Eigenvalues of the Fisher information matrix are stratified according to a sequence of transcendence degrees in this invariant algebra, and critical points…

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Sampling from the SK measure via algorithmic stochastic localization

Ahmed El Alaoui (Cornell University)
E18-304

Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of SK measures tilted by an appropriate external field. This approach is general and can potentially be applied to other discrete or continuous non-log-concave problems. We show that the algorithm outputs a sample within vanishing rescaled Wasserstein…

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Inference in High Dimensions for (Mixed) Generalized Linear Models: the Linear, the Spectral and the Approximate

Marco Mondelli (Institute of Science and Technology Austria)
E18-304

Abstract: In a generalized linear model (GLM), the goal is to estimate a d-dimensional signal x from an n-dimensional observation of the form f(Ax, w), where A is a design matrix and w is a noise vector. Well-known examples of GLMs include linear regression, phase retrieval, 1-bit compressed sensing, and logistic regression. We focus on the high-dimensional setting in which both the number of measurements n and the signal dimension d diverge, with their ratio tending to a fixed constant.…

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Distance-based summaries and modeling of evolutionary trees.

Julia Palacios (Stanford University)
E18-304

Abstract:  Phylogenetic trees are mathematical objects of great importance used to model hierarchical data and evolutionary relationships with applications in many fields including evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explore the posterior distribution of trees via Markov Chain Monte Carlo methods, however assessing uncertainty and summarizing distributions remains challenging for these types of structures. In this talk I will first introduce a distance metric on the space of unlabeled ranked tree shapes and genealogies. I will then…

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Coding convex bodies under Gaussian noise, and the Wills functional

Jaouad Mourtada (ENSAE Paris)
E18-304

Abstract: We consider the problem of sequential probability assignment in the Gaussian setting, where one aims to predict (or equivalently compress) a sequence of real-valued observations almost as well as the best Gaussian distribution with mean constrained to a general domain. First, in the case of a convex constraint set K, we express the hardness of the prediction problem (the minimax regret) in terms of the intrinsic volumes of K. We then establish a comparison inequality for the minimax regret…

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