Innovations in Nonparametric and Functional Data Methods: Tackling Complex Data Challenges

Didong Li Chair
 
Xinyi Li Organizer
Clemson University
 
Thursday, Aug 7: 8:30 AM - 10:20 AM
0454 
Invited Paper Session 
Music City Center 
Room: CC-102B 

Applied

Yes

Main Sponsor

Section on Nonparametric Statistics

Co Sponsors

Biometrics Section
Mental Health Statistics Section

Presentations

Unveiling Mental Health Signals on Social Media Using Functional Data Techniques

The COVID-19 pandemic has precipitated a significant mental health crisis, notably impacting young adults. With the rapid advancement of technology and the ubiquitous use of social media among this demographic, there has been a marked increase in the expression of emotions and mental health concerns on these platforms. We propose methods to study trends in mental health issues, self-harm, and violence towards others as conveyed through social media posts. Traditional methods of analyzing such data often lack interpretability, high computational demands, or inflexibility in data handling. In this work, we develop a flexible statistical framework designed to analyze high-resolution data from social media, aiming to identify users exhibiting atypical posting behaviors.
 

Speaker

Ana Maria Staicu, North Carolina State University

Nonlinear Functional PCA for Functional Data via Neural Networks

Functional principal component analysis (FPCA) is a critical technique for dimension reduction in functional data analysis (FDA). Traditional FPCA methods assume a linear structure in the observed functional data, which may not always hold, leading to inefficiencies when the data exhibits nonlinear characteristics. In this study, we propose a novel FPCA method that accommodates nonlinear structures using neural networks. We design networks specifically for functional data and explore their universal approximation properties. We conduct a simulation study to evaluate the performance of our method and apply it to a real-world dataset to further demonstrate its effectiveness. This talk is based on joint work with Rou Zhong and Jingxiao Zhang. 

Keywords

Curve reconstruction

Nonlinear dimension reduction

Unsupervised learning 

Speaker

Chunming Zhang, University of Wisconsin-Madison

Linear regression using Hilbert-space valued covariates with unknown reproducing kernel

In this talk we present a new method of linear regression using Hilbert-space valued covariates with unknown reproducing kernels. We develop a computationally efficient approach to estimation and derive asymptotic theory for the regression parameter estimates under mild assumptions. We demonstrate the approach in simulation studies as well as in a data analyses using two- and three-dimensional brain images as predictors.  

Co-Author(s)

Xinyi Li, Clemson University
Margaret Hoch
Michael Kosorok, University of North Carolina at Chapel Hill

Speaker

Xinyi Li, Clemson University

Semiparametric Regression Analysis of Interval-Censored Multi-State Data with An Absorbing State

In studies of chronic diseases, the health status of a subject can often be characterized by a finite number of transient disease states and an absorbing state, such as death. The times of transitions among the transient states are ascertained through periodic examinations and thus interval-censored. The time of reaching the absorbing state is known or right-censored, with the transient state at the previous instant being unobserved. We provide a general framework for analyzing such multi-state data. We formulate the effects of potentially time-dependent covariates on
the multi-state disease process through semiparametric proportional intensity models with random effects. We combine nonparametric maximum likelihood estimation with sieve estimation and develop a stable expectation-maximization algorithm. We establish the asymptotic properties of the proposed estimators and assess the performance of the proposed methods through extensive simulation studies. Finally, we provide an illustration with
a cardiac allograft vasculopathy study. 

Keywords

Multi-state model

Interval censoring

Nonparametric maximum likelihood estimation

Semiparametric efficiency

EM algorithm 

Speaker

Donglin Zeng, University of Michigan