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…

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…

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…

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…

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…