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What is Learnable in Valiant's Theory of the Learnable? 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Statistical Analysis of Multi-Relational Network Recovery
Zhi Wang, Xueying Tang, Jingchen Liu · 2020-08-30 · via math.ST updates on arXiv.org

In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum likelihood estimators when the size of the network tends to infinity. The basic technique is to develop a non-asymptotic error bound for the maximum likelihood estimators through large deviations analysis of random fields. We also show that these estimators are nearly optimal in terms of minimax risk.

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