Positive definite kernels applied to probability and statistics: MMD, HSIC and point process

• Grant number: 21/04226-0
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: December 01, 2021
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jean Carlo Guella
• Grantee: Jean Carlo Guella
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated researchers: Guilherme Vieira Nunes Ludwig ; Nancy Lopes Garcia
• Associated scholarship(s): 22/09840-0 - Applications of positive definite kernels in probability, BP.MS; 22/00008-0 - Positive definite kernels applied to probability and statistics: MMD, HSIC and point process, BP.JP

Abstract

In this research project, we aim to develop, apply and improve techniques from approximation theory to problems in statistics and probability, with an emphasis on positive definite kernels. Among the problems we aim to analyze is metrics in probability, independence tests, and conditional independence tests. We also want to develop techniques to analyze the relations between point processes on general spaces using positive definite kernels, with an emphasis on hyperbolic spaces. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GUELLA, JEAN CARLO. Generalization of the HSIC and distance covariance using PDI kernels. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, v. 17, n. 4, p. 53-pg., 2023-10-01. (21/04226-0, 22/00008-0)