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SUMMARY:On optimal ranking in crowd-sourcing problems in several scenarios
  - Alexandra Carpentier\, University of Potsdam
DTSTART:20240517T130000Z
DTEND:20240517T140000Z
UID:TALK213466@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Consider a crowd sourcing problem where we have n experts and 
 d tasks. The average ability of each expert for each task is stored in an 
 unknown matrix M\, from which we have incomplete and noise observations. W
 e make no (semi) parametric assumptions\, but assume that the experts can 
 be perfectly ordered: so that if an expert A is better than an expert B\, 
 the ability of A is higher than that of B for all tasks. We either assume 
 the same for the task\, or not\, depending on the scenario. This implies t
 hat if the matrix M\, up to permutations of its rows and columns\, is eith
 er isotonic\, or bi-isotonic.\n\nWe focus on the problem of recovering the
  optimal ranking of the experts and/or of the tasks\, in l2 norm. We will 
 consider this problem with some side-information — i.e. when the orderin
 g of the tasks (if it exists) is known to the statistician - or not. In ot
 her words\, we aim at estimating the suitable permutation of the rows of M
 . We provide a minimax-optimal and computationally feasible method for thi
 s problem in three scenarios of increasing difficulty: known order of the 
 task\, unknown order of the tasks\, no order of the tasks. The algorithms 
 we provide are based on hierarchical clustering\, PCA\, change-point detec
 tion\, and exchange of informations among the clusters.\n\nThis talk is ba
 sed on a joint ongoing work with Emmanuel Pilliat\, Maximilian Graf and Ni
 colas Verzelen.
LOCATION:MR12\, Centre for Mathematical Sciences
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