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# Statistical and Computational Rates in Graph Logistic Regression

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:2719-2730, 2020.

#### Abstract

We consider the problem of graph logistic regression, based on partial observation of a large network, and on side information associated to its vertices. The generative model is formulated as a matrix logistic regression. The performance of the model is analyzed in a high-dimensional regime under a structural assumption. The optimal statistical rates are derived, and an estimator based on penalized maximum likelihood is shown to attain it. The algorithmic aspects of this problem are also studied, and optimal rates under computational constraints are derived, and shown to differ from the information-theoretic rates - under a complexity assumption.