FRG Informal Talk Series: Yichao Wu and Youhan Lu, UIC Dept. of Math, Stat, and CS.

2:00-2:10pm Lighting talk by Youhan Lu

Title: A Unified Approach to Variable Selection for Partially Linear Models

Abstract: We focus on the general partially linear model without any structure assumption on the nonparametric component. For such a model with both linear and nonlinear predictors being multivariate, we propose a new variable selection method. Our new method is a unified approach in the sense that it can select both linear and nonlinear predictors simultaneously by solving a single optimization problem. We prove that the proposed method achieves consistency. Both simulation examples and a real data example are used to demonstrate the new method’s competitive finite-sample performance.

2:10-3:00pm Informal talk by Prof. Yichao Wu

Title: Variable selection for Fréchet regression

Abstract: Global Fréchet 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 Fréchet regression. Due to the metric space-valued nature of the responses, Fréchet 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 Fréchet regression. In this work, we address this challenge and propose a novel variable selection method that overcomes it and has 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 data illustrations.

References: Tucker, D.C., Wu, Y. and Müller, H.G., 2023. Variable selection for global Fréchet regression. Journal of the American Statistical Association, 118(542), pp.1023-1037.