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Statistics Seminar

Wednesday, March 23rd, 2022

Time: 10:00 a.m.  Place: Online via Zoom (contact Brian Ling for Zoom link)

Speaker: Na Li (Queen's University)

Title: Bootstrap adjustment for predictive classification

Abstract: In clinical practice, it is important to identify a subgroup of patients who may benefit more in terms of a clinical outcome from a given treatment. The subgroup is usually induced by a continuous predictive biomarker and an associated unknown cutpoint, and this predictive classification problem is formulated as testing the significance of the interaction between the treatment and the subgroup indicator. Two commonly adopted procedures, minimum p-value and profile tests, are not reliable due to the inflated Type I error and/or identifiability issues. We propose bootstrap-based adjustments for various types of outcomes and establish their asymptotic validity. The proposed methods are applied to clinical trial data.

Curves Seminar

Monday, March 21st, 2022

Time: 11:00 a.m.  Place: Jeffery Hall Room 222, or Online via Zoom (contact Deepanshu Prasad for Zoom link)

Speaker: Alexandre (Sasha) Zotine

Title: Broken Circuit Complexes for a Matroids

Abstract: In this talk, we'll introduce broken circuits, broken circuit complexes, and relate the coefficients of the characteristic polynomial of a matroid to its broken circuit complexes.

Math & Stats Department Colloquium

Friday, March 25th, 2022

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Peter Olver (University of Minnesota)

Title: Fractalization and Quantization in Dispersive Systems

Abstract: The evolution, through spatially periodic linear dispersion, of rough initial data produces fractal, non-differentiable profiles at irrational times and, for asymptotically polynomial dispersion relations, quantized structures at rational times. Such phenomena have been observed in dispersive wave models, optics, and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications and recent progress on the analysis, numerics, and extensions to nonlinear wave models, both integrable and non-integrable, will be presented. Time permitting, recent related results for the Fermi-Pasta-Ulam problem will also be discussed.

Peter Olver is a Full Professor in the School of Mathematics at the University of Minnesota since 1985. He served as the Head of the Department from 2008 to 2020. He is a Fellow of the American Mathematical Society, the Society for Industrial and Applied Mathematics (SIAM), and the Institute of Physics, UK. His research interests revolve around the applications of symmetry and Lie groups to differential equations. Over the years, he has contributed to a wide range of fields, including mathematical physics, fluid mechanics, elasticity, quantum mechanics, Hamiltonian mechanics, the calculus of variations, differential geometry, classical invariant theory, computer vision, geometric numerical methods.

Statistics Seminar

Wednesday, March 16th, 2022

Time: 10:00 a.m.  Place: Online via Zoom (contact Brian Ling for Zoom link)

Speaker: Guanhua Fang (Baidu USA)

Title: Advances in Machine Learning with Heavy-tailed Distributions

Abstract: In many fields such as telecommunications, survival analysis, quality control, online recommendation, and reinforcement learning, one often encounters situations where the data sources behave normally most of the time, but sometimes could become hetero genous and unstructured. Learning in these applications should consider reward distributions with tails heavier than the normal distribution.

In the literature, a remarkable M-estimator proposed by Catoni (2012) has been shown to be rate-optimal in mean estimation problems with finite variance condition. During this talk, I will discuss more advanced statistical learning results based on Catoni-type estimators especially in the situations with infinite variance or presence of contaminated observations. Several interesting applications are given to show how new theory can be adapted into machine learning tasks to achieve better performance.

Math & Stats Department Colloquium

Friday, March 18th, 2022

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Kengo Kato (Cornell University)

Title: Scalable statistical theory for smooth Wasserstein distances

Abstract: The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked by the curse of dimensionality, whereby the number of data points needed to accurately estimate them grows exponentially with dimension. Gaussian smoothing was recently introduced as a means to alleviate the curse of dimensionality, giving rise to a parametric convergence rate in any dimension, while preserving the Wasserstein metric and topological structure. To facilitate valid statistical inference, in this work, we develop a comprehensive limit distribution theory for the empirical smooth Wasserstein distance. The limit distribution results leverage the functional delta method after embedding the domain of the Wasserstein distance into a certain dual Sobolev space, characterizing its Hadamard directional derivative for the dual Sobolev norm, and establishing weak convergence of the smooth empirical process in the dual space. To estimate the distributional limits, we also establish consistency of the nonparametric bootstrap. Finally, we use the limit distribution theory to study applications to generative modeling via minimum distance estimation with the smooth Wasserstein distance, showing asymptotic normality of optimal solutions for the quadratic cost.

Kengo Kato is a Full Professor in the Department of Statistics and Data Science at Cornell University. Prior to Cornell, he was an Associate Professor in the Graduate School of Economics at the University of Tokyo. His research interests include mathematical statistics, econometrics, quantile regression, high-dimensional/nonparametric statistics. He receives many awards, including Analysis Award (2021), Japan Academy Medal (2020), JSPS Prize (2020).

Workshop on Mathematical Ecology

August 10th-11th, 2022

Algebra & Geometry Seminar

Monday, March 28th, 2022

Time: 4:30 p.m.  Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)

Speaker: Magdalena Boos (Ruhr-Universität Bochum)

Title: Symmetric quiver representations and degenerations.

Abstract: The notion of a symmetric quiver was first introduced by Derksen and Weyman in 2002. Symmetric quiver representations are collected in so-called symmetric representation varieties which are acted on by reductive groups via change of basis. We are interested in the orbits and their closures of said actions. Orbit closure relations lead us to considering symmetric degenerations for which one of the most important questions is: are symmetric degenerations induced by “usual” degenerations in the representation variety of the underlying quiver? We look at (counter)examples and recent results. This is joint work with G. Cerulli Irelli.

Website details here:

Algebra & Geometry Seminar

Monday, March 21st, 2022

Time: 4:30 p.m.  Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)

Speaker: Marco Antonia Armenta (Université de Sherbrooke)

Title: Double framed moduli spaces of quiver representations and applications to neural networks.

Abstract: I will present an introduction to the study of neural networks using double framed quiver representations and show why it is important for these applications to understand the structure of moduli spaces of these types of representations. I will give both a linear algebra description and a representation-theoretic description of these moduli spaces and then show that the output of a neural network depends only on the corresponding point in the moduli space. There is no need to know anything about neural networks to follow this talk as I will give you all the necessary definitions.

Website details here:

Curves Seminar

Monday, March 14th, 2022

Time: 11:00 a.m.  Place: Jeffery Hall Room 222, or Online via Zoom (contact Deepanshu Prasad for Zoom link)

Speaker: Cody Roth

Title: Structure of Orlik Solomon Algebra for Central Arrangements

Abstract: We will show that given any nonempty central arrangement, the $\mathcal{K}$-linear boundary map on $\mathcal{E}$, the exterior algebra formed from the arrangement, can be naturally defined on the corresponding Orlik-Solomon algebra $\mathcal{A}$, and this definition gives an acyclic chain complex $(\mathcal{A}, \partial)$. We also show how $\mathcal{A}$ can be decomposed into a direct sum indexed via the intersection poset of the arrangement.