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Logistics: 11:30am-12:30pm, RE036
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
Logistics: 12:45pm-1:45pm, RE-TBD
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
Logistics: 11:30am-12:30pm, RE036
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
Logistics: 11:30am-12:30pm, RE112
Abstract: coming soon!
Selected (local) algebraic statistics activities
Join us at IMSI in Fall 2023!!
This algebraic statistics community homepage has several important recent announcements.
Nonlinear algebra and statistics (NLASTATS) seminar, and updated version of the old alg stats seminar, started in Fall 2019. Find upcoming and past talks here; .... but apparently IIT made another unfortunate decision: to only keep a record of most recent past talks! How annoying? As of 2023, I will keep my own record here!
Fall 2013 - Fall 2018, the Algebraic Statistics seminar took place weekly at IIT. As of 2016, events are announced on the Department Events page; previous semesters can be found here: Algebraic Statistics seminar pages.
Many conferences include special sessions on Algebraic statistics:
The 2023 JSM in Toronto has a topic-contributed session Algebraic and geometric methods in inference;
The 2016 Joint Statistics Meetings hosted an IMS-sponsored Topic-Contributed Paper Session: Algebraic and geometric methods in inference - two decades of algebraic statistics, in July 2016 in Chicago;
The 2015 AMS Fall Central Section Meeting in Chicago included a special session on algebraic statistics;
and many more.
In May 2014, IIT hosted the 2014 Algebraic Statistics conference, which continues the tradition of biennial algebraic statistics meetings in the US. The previous such meeting took place in June 2012, hosted by Penn State. The Algebraic Statistics in the Alleghenies conference was supported by the NSF, Packard Foundation, the Eberly College of Science, and the Mathematics and Statistics Departments at Penn State.
In winter 2011/2012, I was named a co-Editor-in-Chief of the Journal of Algebraic Statistics. IIT Library took over hosting the journal in 2015. The journal was discontinued after we published its final volume, in memory of Stephen E. Fienberg in 2019.
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.