위상 기반 통계 및 인공지능 연구실

연구실 소개

The Topological Statistics and Artificial Intelligence Lab primarily researches methods for statistically estimating Topological Data Analysis (TDA) and applying it to machine learning or data analysis. In the field of mathematics, topology explores how local parts are globally connected, and utilizing these topological characteristics in data analysis is called Topological Data Analysis. We study statistical methods and related theories for inferring such topological data analysis from data under a statistical model. To this end, we develop theories of computational topology suitable for situations that require estimating topological structures from data, and also extend existing statistical theories to meet the topological and geometric conditions required by topological data analysis. Additionally, we concurrently research practical applications of topological data analysis to machine learning or data analysis.