Model Selection in Algebraic Pattern Recognition

• Activity Number: 321 - Machine Learning and Variable Selection
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Qida Ma* and David Kahle
• Companies: Microsoft and Baylor University
• Keywords: Varieties; Model Selection; Algebraic Pattern Recognition; Monte Carlo Simulation

Abstract

Nonlinear polynomial equations are found throughout applied science. In many cases, these equations describe positive-dimensional solution sets called real varieties that in general may be quite complex but locally look like smooth manifolds almost everywhere. In this presentation we describe model selection strategies for recovering algebraic patterns, represented as the solution sets of a multivariate polynomials, when a cloud of points near the polynomial’s corresponding variety are presented. Several examples are provided using synthetic datasets whose points fall near common varieties.