Expert-ranking for bi-isotonic matrices under unknown permutations

03.07.2023, 10:15  –  Golm, Haus 9, Raum 1.10
Forschungsseminar Statistik

Max Graf

Abstract:  

 As motivation, we consider a bunch of experts responding to a set of questions, where we can observe whether an expert answers a question correctly or not. Assume that for every pair of experts, one of the experts has for every question at least the same probability to answer correctly as the other expert. This means that they can be ordered by quality, and moreover we assume that the questions can be ordered by difficulty in the same sense. Storing the probabilities of a correct answer yields a matrix, where each row corresponds to an expert and each column corresponds to a question. By assumption, this matrix can be ordered such that each row and column is non-decreasing. We call such a matrix bi-isotonic.
In contrast to the last talk, I will explain the sequential observation model and present an algorithm that approximately sorts experts by quality. Using a Bernstein-type inequality, I will illustrate how high probability upper bounds for the permutation error can be derived.