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Optimal Link Prediction with Matrix Logistic Regression

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STSW01 - Theoretical and algorithmic underpinnings of Big Data

We consider the problem of link prediction, based on partial observation of a large network and on covariates associated to its vertices. The generative model is formulated as matrix logistic regression. The performance of the model is analysed in a high-dimensional regime under structural assumption. The minimax rate for the Frobenius norm risk is established and a combinatorial estimator based on the penalised maximum likelihood approach is shown to achieve it. Furthermore, it is shown that this rate cannot be attained by any algorithm computable in polynomial time, under a computational complexity assumption. (Joint work with Nicolai Baldin)

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