Title: Optimal link prediction with matrix logistic regression
Authors: Quentin Berthet - University of Cambridge (United Kingdom) [presenting]
Nicolai Baldin - University of Cambridge (United Kingdom)
Abstract: The problem of link prediction is considered 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 analysed in a high-dimensional regime under a 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 (randomised) algorithm computable in polynomial time under a computational complexity assumption.