• 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.

• 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. 

• 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.

• Logistics: 11:30am-12:30pm, RE112

Title: tbd
Abstract: coming soon!