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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Optimal rates for ranking a permuted isotonic matrix in polynomial time

Résumé

We consider a ranking problem where we have noisy observations from a matrix with isotonic columns whose rows have been permuted by some permutation π *. This encompasses many models, including crowd-labeling and ranking in tournaments by pair-wise comparisons. In this work, we provide an optimal and polynomial-time procedure for recovering π * , settling an open problem in [7]. As a byproduct, our procedure is used to improve the state-of-the art for ranking problems in the stochastically transitive model (SST). Our approach is based on iterative pairwise comparisons by suitable data-driven weighted means of the columns. These weights are built using a combination of spectral methods with new dimension-reduction techniques. In order to deal with the important case of missing data, we establish a new concentration inequality for sparse and centered rectangular Wishart-type matrices.
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hal-04223348 , version 1 (29-09-2023)

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Emmanuel Pilliat, Alexandra Carpentier, Nicolas Verzelen. Optimal rates for ranking a permuted isotonic matrix in polynomial time. 2023. ⟨hal-04223348⟩
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