Ranking from Pairwise Comparisons in General Graphs and Graphs with Locality. (arXiv:2304.06821v1 [stat.ML])

This technical report studies the problem of ranking from pairwise
comparisons in the classical Bradley-Terry-Luce (BTL) model, with a focus on
score estimation. For general graphs, we show that, with sufficiently many
samples, maximum likelihood estimation (MLE) achieves an entrywise estimation
error matching the Cram\'er-Rao lower bound, which can be stated in terms of
effective resistances; the key to our analysis is a connection between
statistical estimation and iterative optimization by preconditioned gradient
descent. We are also particularly interested in …

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