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Abstract:
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Prediction problems typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors, information on the subjects' social networks is often available and plays an important role through network cohesion, the empirically observed phenomenon of friends behaving similarly. Taking cohesion into account in prediction models should allow us to improve their performance. Here we propose a regression model with a network-based penalty on individual node effects to encourage similarity between predictions for linked nodes, and show that it performs better than traditional models both theoretically and empirically when network cohesion is present. The framework is easily extended to other models, such as the generalized linear model and Cox's proportional hazard model. Applications to predicting levels of recreational activity and marijuana usage among teenagers based on both demographic covariates and their friendship networks are discussed in detail and demonstrate the effectiveness of our approach. This is joint work with Tianxi Li and Elizaveta Levina.
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