NLAStats seminar 

Sign up for our mailing list:

Spring 2023

3/3/23 Aida Maraj, University of Michigan

Title: Staged Tree Models with Toric Structure 

Abstract: Staged tree models are discrete statistical models encoding relationships between events that generalize Bayesian networks. Relationships between events are encoded in a directed rooted tree with colored vertices. These event based models are often used in public health, medicine, risk analysis and policing.  In algebro-geometric terms, the model consists of points inside a toric variety whose design matrix is determined by the root to leaf paths in the tree. For certain trees, called balanced, Duarte and Görgen proved that the model is in fact the intersection of the toric variety and the probability simplex. The toric structure gives the model a straightforward description, and has computational advantages; it provides a Gröbner basis of binomial quadratics completely determined by the paths in the tree. In this talk we show that the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. The change of coordinates and the new binomial equation rely on the combinatorics of the tree. The talk is based on joint work with Christiane Görgen and Lisa Nicklasson.

4/12/23 Ivan Gvozdanovic, Applied Mathematics student, IIT

Title: Introduction to Reinforcement Learning and its Application in Economics.
Abstract: Reinforcement Learning has been a prominent area of research for the last 2 decades. It has seen major expansion in recent times with the development of Neural Networks and more powerful computing machines. One of the most desirable aspects of RL, can be found in the class of model-free algorithms which can learn optimal policies without the knowledge of the underlying data generation process. We split this talk into 2 parts. The first part constitutes the formulation of a discrete time Markov Decision Process as the basis of RL. We provide an overview of two groups of classical RL algorithms, value-based and policy-based. In the second part, we present our latest work in the development of algorithms designed to approximate solutions to recursive economic utility such as Epstein-Zin (EZ) utility preference. We compare and contrast their convergence properties on the optimal consumption portfolio problem with an EZ utility. This is joint work with Professor Matthew Dixon. 

4/7/23 Félix Almendra-Hernández, University of California Davis

Title: Algebraic methods in statistics: an exploration of Markov bases
Abstract: The concept of Markov basis was first introduced by Diaconis and Sturmfels as a means of using algebraic methods to perform exact tests on discrete exponential families. While certain statistical models possess compact Markov bases, such as decomposable models as illustrated by Dobra, non-decomposable models present significant challenges, as exemplified by De Loera and Onn. This talk presents our contributions to the understanding of the good and bad behavior of Markov basis, with a focus on two specific models. In the first part, we provide a simple Markov basis for the beta Stochastic Block Model. In the second part, we explore the limitations of non-negative relaxation on table entries in the no-three-way interaction model. These findings are the result of collaborative work with Prof. Jesus De Loera and Prof. Sonja Petrović.

5/3?/23 Amirreza Eshraghi, Applied Mathematics student, IIT

Title: tbd
Abstract: coming soon! 

Selected (local) algebraic statistics activities

Algebraic statistics is a relatively young research area, attracting many researchers from both statistics and mathematics communities. The SIAM activity group in algebraic geometry has many members interested in algebraic statistics. The biennial SIAG meeting usually features multiple minisymposia in the field. National and regional AMS meetings, as well as recent and upcoming national and international IMS and JSM meetings, include special sessions on the topics of theoretical and applied algebraic statistics. In 2014, there was also an algebraic session organized at Computational Statistics meeting COMPSTAT, and in 2015 a special session at the ISI World Statistics Congress. 2014 has been a very busy year for algebraic statistics conferences: Kyoto in January, Chicago in May, NIMS in Korea in July, Prague in August.

The field continues to be visibly active, with dedicated conferences every (other) year: as2012 at Penn State, as2014 at IIT, as2015 in Genova, Italy, as2022 in Hawaii. 2016 was the year we organized an AMS Mathematical Research Community (MRC) program on algebraic statistics.