Cohesive Regression Over Networks

• Activity Number: 378
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 11:35 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Tianxi Li* and Elizaveta Levina and Ji Zhu
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Network ; Regression ; Prediciton

Abstract

In regression problems, networks among individual samples are available in many data sets nowadays. Network connections may represent similarity between nodes. Such effect is called network cohesion in social analysis. General approaches to incorporate such salient information in regression models have been rarely discussed in previous literature. We propose a framework to fit heterogeneous regression models for all nodes but encourage connected nodes to have similar regression curves. Both finite-sample model estimation error bound and asymptotic covariate effects estimation consistency are established. Applications to spatial missing data imputation and predicting substance abuse level of adolescents by using the friendship network demonstrate the effectiveness of the model as well.