Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung

By E. Zermelo. 1929

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Citations in the corpus

Generalized Results for the Existence and Consistency of the MLE in the Bradley-Terry-Luce Model (2021, background): “As proved by Zermelo (1929) and Ford Jr (1957), this is indeed sufﬁcient and necessary for a unique solution.”
Computational and Statistical Tradeoffs in Learning to Rank (2016, methodology): “e can resort to faster methods with smaller M while achieving the same level of accuracy. Learning to rank from the PL model has been studied extensively under the traditional scenario dating back to Zermelo (1929) who rst introduced the PL model for pairwise comparisons. Various approaches for esti”
Probability Estimates for Multi-class Classification by Pairwise Coupling (2003, background): “It points out that [23] has proved that, for any initial point, the whole sequence generated by Algorithm 1 converges to a point satisfying (2.”
Matrix estimation by Universal Singular Value Thresholding (2012, methodology): “for (generalized) Bradley-Terry models [3, 50, 51, 52, 54, 30]. For the basic Bradley-Terry model, it is possible to nd the maximum likelihood estimate of the a i’s using a simple iterative procedure [100, 61, 69]. The maximum likelihood estimate was shown to be jointly consistent for all nparameter”
A Generalization of the Dirichlet Distribution (2010, unknown): “When P i plays P j with i = j, the result is a single observation from a Bernoulli distribution with parameters p i p i +p j , p j p i +p j (Zermelo 1929), where the p i are the unknown probabilities of victory; we require p i = 1.”
Fast and Accurate Inference of Plackett-Luce Models (2015, methodology): “In the special case of pairwise comparisons, the same iterative algorithm was independently discovered by Zermelo [15], Ford [16] and Dykstra [17].”
Post Classification Label Refinement Using Implicit Ordering Constraint Among Data Instances (2015, methodology): “Hence, methods that use pairwise preference relationships can be potentially used to estimate total ordering [11], [8], [9], [12], [13], [14].”
GROUPED SPARSE PAIRED COMPARISONS IN THE BRADLEY-TERRY MODEL (2011, background): “The likelihood equation is ai = t∑ j=0 nij ûi ûi + ûj i = 1, . . . , t. (2.2) By Zermelo (1929) and Ford (1957), the following condition guarantees the existence and uniqueness of the MLEs in (2.1).”
MM algorithms for generalized Bradley-Terry models (2003, methodology): “A simple iterative algorithm for finding maximum likelihood estimates in the Bradley-Terry model has been known for a long time (Zermelo 1929).”