Data Analysis with Statistical Information Theory

Speaker:Prof. Alejandro C. Frery (Universidade Federal de Alagoas)

Time and Date: 9:00-11:30, Oct. 10, 2016

Place: Room 1101, East Main Building of Guanghua Tower, Handan Campus

 

 

Abstract

The Statistical Information Theory produces, among other tools, statistical tests to verify if two or more samples come from the same distribution. This is a classical problem in Statistics, and the KS, t, chi-squared, F, and likelihood ratio tests are some of the basic tools one has to solve it. Although widespread due to their good performance, these tests are limited to relatively simple situations, and their discrimination ability may be severely impaired when the data do not follow the hypothesis under which they were derived. Many applications rely on the use of measures of dissimilarity, oftentimes distances, to decide if two or more samples were produced by the same probability law. Distances are flexible tools, but they seldom produce rich semantic results: "near vs. far" is less expressive than "reject vs. do not reject the hypothesis that the samples come from the same distribution". Recent results from the Statistical Information Theory realm provide powerful tools by endowing a large class of distances with semantic contents. This is the case of the stochastic h-phi distances, and the differences of h-phi entropies. These families of test statistics are a promising venue for both theoretical studies and applications. In this talk we will revise the main concepts underlying these new tools, and we will see how eight seemingly different problems in image processing and analysis (feature extraction, hierarchical segmentation, classification, noise reduction, spectral decomposition, parameter estimation, edge and change detection) can be formulated and solved within this context.

 

 

Biography

Alejandro Frery received the B.S. degree in electronic and electrical engineering from the Universidad de Mendoza, Mendoza, Argentina, the M.Sc. degree in applied mathematics (statistics) from the Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, and the Ph.D. degree in applied computing from the Instituto Nacional de Pesquisas Espaciais, São José dos Campos, Brazil.He is currently with the Instituto de Computação, Universidade Federal de Alagoas, Maceió, Brazil. His research interests are statistical computing and stochastic modeling.