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Mathematics > Statistics Theory

Title: Optimal link prediction with matrix logistic regression

Abstract: We consider the problem of link prediction, 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.
Subjects: Statistics Theory (math.ST); Machine Learning (stat.ML)
MSC classes: 62J02, 62C20 (Primary) 68Q17 (Secondary)
Cite as: arXiv:1803.07054 [math.ST]
  (or arXiv:1803.07054v1 [math.ST] for this version)

Submission history

From: Nicolai Baldin [view email]
[v1] Mon, 19 Mar 2018 17:32:50 GMT (72kb)