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

• Grant number: 22/00008-0
• Support Opportunities: Scholarships in Brazil - Young Researchers
• Start date: January 01, 2022
• 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 research grant: 21/04226-0 - Positive definite kernels applied to probability and statistics: MMD, HSIC and point process., AP.JP

Abstract

Neste projeto de pesquisa pretendemos desenvolver, aplicar e aprimorar técnicas de teoria de aproximação para problemas estatísticos e probabilísticos, tendo como enfoque os núcleos positivos definidos. Dentre os problemas a serem analisados estão: distancia entre probabilidades, testes de independência e independência condicional. Também pretendemos obter técnicas afim de se analisar a relação entre processos pontuais em espaços mais gerais usando núcleos positivos definidos, com um enfoque em espaços hiperbólicos.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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)

GUELLA, JEAN CARLO. Hilbert space embeddings of independence tests of several variables with radial basis functions. ANALYSIS AND APPLICATIONS, v. N/A, p. 55-pg., 2025-11-04. (22/00008-0, 21/04226-0)