Prediction models with graph kernel regularization for network data

Abstract

Traditional regression methods typically consider only covariate information and assume that the observations are mutually independent samples. However, samples usually come from individuals connected by a network in many modern applications. We present a risk minimization formulation for learning from both covariates and network structure in the context of graph kernel regularization. The formulation involves a loss function with a penalty term. This penalty can be used not only to encourage similarity between linked nodes but also lead to improvement over traditional regression models. Furthermore, the penalty can be used with many loss-based predictive methods, such as linear regression with squared loss and logistic regression with log-likelihood loss. Simulations to evaluate the performance of this model in the cases of low dimensions and high dimensions show that our proposed approach outperforms all other benchmarks. We verify this for uniform graph, nonuniform graph, balanced-sample, and unbalanced-sample datasets. The approach was applied to predicting the response values on a ‘follow’ social network of Tencent Weibo users and on two citation networks (Cora and CiteSeer). Each instance verifies that the proposed method combining covariate information and link structure with the graph kernel regularization can improve predictive performance.

Keywords:

• Graph regularization
• node effect
• kernel function
• prediction
• regression

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) [grant number 71771201], [grant number 71874171], [grant number 71731010], [grant number 71631006], [grant number 71991464], [grant number 71871208] and [grant number 72071193], Anhui Provincial Natural Science Foundation, the Ministry of Education Humanities and Social Science Project of China [grant number 20YJA910006], Natural Science Foundation of Jiangsu Province (No. BK20201396), and Natural Science Foundation of the Higher Education Institutions of Jiangsu Province [grant number 19KJA180003].