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CATEGORIES:Statistics
SUMMARY:On optimal ranking in crowd-sourcing problems in s
everal scenarios - Alexandra Carpentier\, Universi
ty of Potsdam
DTSTART;TZID=Europe/London:20240517T140000
DTEND;TZID=Europe/London:20240517T150000
UID:TALK213466AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/213466
DESCRIPTION:Consider a crowd sourcing problem where we have n
experts and d tasks. The average ability of each e
xpert for each task is stored in an unknown matrix
M\, from which we have incomplete and noise obser
vations. We make no (semi) parametric assumptions\
, but assume that the experts can be perfectly ord
ered: so that if an expert A is better than an exp
ert B\, the ability of A is higher than that of B
for all tasks. We either assume the same for the t
ask\, or not\, depending on the scenario. This imp
lies that if the matrix M\, up to permutations of
its rows and columns\, is either 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 stat
istician - or not. In other words\, we aim at esti
mating the suitable permutation of the rows of M.
We provide a minimax-optimal and computationally f
easible method for this problem in three scenarios
of increasing difficulty: known order of the task
\, unknown order of the tasks\, no order of the ta
sks. The algorithms we provide are based on hierar
chical clustering\, PCA\, change-point detection\,
and exchange of informations among the clusters.\
n\nThis talk is based on a joint ongoing work with
Emmanuel Pilliat\, Maximilian Graf and Nicolas Ve
rzelen.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Dr Sergio Bacallado
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