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New directions in algebraic statistics: Three challenges from 2023

Yulia Alexandr, Miles Bakenhus, Maize Curiel, Sameer K. Deshpande, Elizabeth Gross, Yuqi Gu, Max Hill, Joseph Johnson, Bryson Kagy, Vishesh Karwa, Jiayi Li, Hanbaek Lyu, Sonja Petrović and Jose Israel Rodriguez

Vol. 15 (2024), No. 2, 357–382
Abstract

In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical and computational statistics. These developments have found applications in a growing number of areas, including biology, neuroscience, economics, and social sciences.

Naturally, new connections continue to be made with other areas of mathematics and statistics. We outline three such connections: to statistical models used in educational testing, to a classification problem for a family of nonparametric regression models, and to phase transition phenomena under uniform sampling of contingency tables. We illustrate the motivating problems, each of which is for algebraic statistics a new direction, and demonstrate an enhancement of related methodologies.

Keywords
algebraic statistics, likelihood geometry, educational measurement, identifiability, regression trees, contingency tables, phase transition
Mathematical Subject Classification
Primary: 62R01
Milestones
Received: 20 February 2024
Revised: 19 June 2024
Accepted: 30 July 2024
Published: 3 December 2024
Authors
Yulia Alexandr
Department of Mathematics
University of California
Los Angeles, CA
United States
Miles Bakenhus
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL
United States
Maize Curiel
Department of Mathematics
University of Hawai‘i at Mānoa
Honolulu, HI
United States
Sameer K. Deshpande
Department of Statistics
University of Wisconsin
Madison, WI
United States
Elizabeth Gross
Department of Mathematics
University of Hawai‘i at Mānoa
Honolulu, HI
United States
Yuqi Gu
Department of Statistics
Columbia University
New York, NY
United States
Max Hill
Department of Mathematics
University of California
Riverside, CA
United States
Joseph Johnson
Institutionen för Matematik
KTH Royal Institute of Technology
Stockholm
Sweden
Bryson Kagy
Department of Mathematics
North Carolina State University
Raleigh, NC
United States
Vishesh Karwa
Department of Statistics, Operations and Data Science
Temple University
Philadelphia, PA
United States
Jiayi Li
Department of Statistics and Data Science
University of California
Los Angeles, CA
United States
Hanbaek Lyu
Department of Mathematics
University of Wisconsin
Madison, WI
United States
Sonja Petrović
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL
United States
Jose Israel Rodriguez
Department of Mathematics
University of Wisconsin
Madison, WI
United States