Posted March 15, 2019

3:30 pm - 4:30 pm Lockett 232
Yichuan Zhao, Georgia State University

Empirical likelihood for the bivariate survival function under univariate censoring

Abstract: The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal approximation method and the adjusted empirical likelihood method in most cases. The Diabetic Retinopathy Data are analyzed for illustration of the proposed procedure. This is joint work with Haitao Huang.

Posted March 26, 2019

3:30 pm - 4:30 pm Lockett 232
Arnab Ganguly, LSU

Reading Group Talk: An introduction to RKHS

Abstract: I will present some introductory materials on Reproducing kernel Hilbert spaces and its use in supervised learning.

Posted April 9, 2019

3:30 pm - 4:30 pm Lockett 232
Arnab Ganguly, LSU

An Introduction to RKHS - Part II

Posted August 9, 2019

Last modified October 31, 2019

Dejan Slepcev, Carnegie Mellon University

Variational problems on random structures: analysis and applications to data science

Abstract: Modern data-acquisition techniques produce a wealth of data about the world we live in. Extracting the information from the data leads to machine learning/statistics tasks such as clustering, classification, regression, dimensionality reduction, and others. Many of these tasks seek to minimize a functional, defined on the available random sample, which specifies the desired properties of the object sought.

I will present a mathematical framework suitable for studies of asymptotic properties of such, variational, problems posed on random samples and related random geometries (e.g. proximity graphs). In particular we will discuss the passage from discrete variational problems on random samples to their continuum limits. Furthermore we will discuss how tools of applies analysis help shed light on algorithms of machine learning.