Prediction algorithms 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 network 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 network-based penalty on individual node effects to encourage
similarity between predictions for linked nodes, and show that incorporating it
into prediction leads to improvement over traditional models both theoretically
and empirically when network cohesion is present. The penalty can be used with
many loss-based prediction methods, such as regression, generalized linear
models, and Cox's proportional hazard model. Applications to predicting levels
of recreational activity and marijuana usage among teenagers from the AddHealth
study based on both demographic covariates and friendship networks are
discussed in detail and show that our approach to taking friendships into
account can significantly improve predictions of behavior while providing
interpretable estimates of covariate effects.

本研究探讨了在众多现代应用中，训练数据中可能存在互相连接的个体不独立样本的情况下，预测算法的表现。我们提出了一种基于网络的罚函数来鼓励联通节点的预测相似性，并证明了将其应用于预测模型能够在现实和理论上得到显著的表现改进，特别在存在网络内部联系的情况下。此罚函数可以与许多基于损失的预测模型相结合，如回归模型，广义线性模型和 Cox 比例危险模型。通过对青少年的探险行为和大麻使用水平的预测研究，我们发现了这种方法对预测行为的提高是有效的，并且提供了对变量效应估计的说明。