Graduate Student Colloquium
Dani Tucker
UIC
Variable Selection for Global Fr\'echet Regression
Abstract: Global Fr\'echet regression is an extension of linear regression to cover more general types of responses, such as distributions, networks and manifolds, which are becoming more prevalent. In such models, predictors are Euclidean while responses are metric space valued. Predictor selection is of major relevance for regression modeling in the presence of multiple predictors but has not yet been addressed for Fr\'echet regression. Due to the metric space valued nature of the responses, Fr\'echet regression models do not feature model parameters, and this lack of parameters makes it a major challenge to extend existing variable selection methods for linear regression to global Fr\'echet regression. In this talk, I will share my work, in collaboration with Yichao Wu (UIC) and Hans-Georg Mueller (UC Davis), which addresses this challenge and proposes a novel variable selection method with good practical performance. We provide theoretical support and demonstrate that the proposed variable selection method achieves selection consistency. We also explore the finite sample performance of the proposed method with numerical examples and real data illustrations. If time permits, I will also briefly share my more recent research that developed as a result of this paper, research which seeks to further generalize global Fr\'echet regression and allow for not only the responses to come from a general metric space, but also the predictors.
Hybrid talk
Monday February 7, 2022 at 5:00 PM in 636 SEO