On Propagated Scoring for Semi-supervised Additive Models

In this paper, a semi-supervised modeling framework that combines feature-based (x) data and graph-based (G) data for classification/regression of the response Y is presented. In this semi-supervised 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 semi-supervised fixed point regularization approach that essentially extends the generalized additive model into the semisupervised setting. In this paper, we first articulate when semi-supervised degeneracies are expected within our framework and then provide a general regularization strategy to address such circumstances. For statistical analysis we establish that the approach uses shrinking smoothers, provide circumstances for when the result is consistent, provide measures of inference and description, and establish clear connections to supervised models. Lastly, several semi-supervised approaches have been considered for the classification problem posed, typically motivated from energy optimization perspective. In this work, we rigorously connect the statistically based propagated ∗Correspondence Information: M. Culp, Department of Statistics, West Virginia University. E-mail: [email protected]. The author thanks the editor, AE and two referees whose suggestions lead to a substantial improvement of this work. 1 scoring framework to this class of approaches. This is particularly insightful, especially with regard to supervised comparisons, since this type of analysis is lacking for the previous work. Two applications are presented, the first involves classification of protein location on a cell using a network of protein interaction data, and the second involves classification of text documents with citation network information and text data. Some key words: Semi-supervised learning; Fixed Point Optimization; Additive Models.