On Propagated Scoring for Semisupervised Additive Models

This article presents a semisupervised modeling framework that combines feature-based (x) data and graph-based (G) data for classification/regression of the response Y. In this semisupervised setting, Y is observed for a subset of the observations (labeled) and missing for the remainder (unlabeled). The Propagated Scoring algorithm proposed for fitting this model is a semisupervised fixed-point regularization approach that essentially extends the generalized additive model into the semisupervised setting. I first articulate when semisupervised degeneracies are expected within my framework, and then provide a general regularization strategy to address such circumstances. For statistical analysis, I establish that the approach uses shrinking smoothers, provide circumstances in which when the result is consistent, provide measures of inference and description, and establish clear connections to supervised models. Several semisupervised approaches have been considered for the classification problem posed, typically motivated from energy optimization perspective. In this work, I rigorously connect the statistically based propagated scoring framework to this class of approaches. This is particularly insightful, especially with regard to supervised comparisons, because this type of analysis is lacking for the previous work. Two applications are presented, one involving classification of protein location on a cell using a network of protein interaction data and the other involving classification of text documents with citation network information and text data. This article has supplementary material online.