Flexible Locally Weighted Penalized Regression with Applications on Prediction of ADNI Clinical Scores

• Activity Number: 506 - Advances in Multivariate Analysis for High-Dimensional, Complex Data Problems
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Peiyao Wang* and Yufeng Liu and Dinggang Shen
• Companies: and University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill
• Keywords: heterogeneity; local models; random forests; ordinal classi cation

Abstract

In recent years we have witnessed the explosion of large-scale data in various fields. Classical statistical methodologies such as linear regression or generalized linear regression often show inadequate performance on heterogeneous data because the key homogeneity assumption fails. In this talk, we will present a flexible framework to handle heterogeneous populations that can be naturally grouped into several ordered subtypes. A local model technique utilizing ordinal class labels during the training stage is proposed. We define a "progression score" that captures the progression of ordinal classes and use a truncated Gaussian kernel to construct the weight function in a local regression framework. Furthermore, given the weights, we apply an Elastic Net shrinkage on the local fitting to handle high dimensionality. In this way, our local model is able to conduct variable selection on each query point. Numerical studies show the superiority of our proposed method over several existing ones. Our method is also applied to the ADNI data to make predictions on the longitudinal clinical scores based on different modalities of baseline brain image features.