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DTSTAMP:20240226T105932Z
SUMMARY:Scalable Inference for Statistical Models of Ranking Data
DESCRIPTION:Speaker: Professor Milan Vojnovic (London School of Economics
& Political Science (LSE))\nAbstract: In this talk\, we present new result
s on the rate of convergence of gradient descent and MM algorithms for fit
ting the parameters of generalised Bradley-Terry models of ranking data\,
including the Bradley-Terry model\, Luce’s choice model\, and Plackett-L
uce ranking model. We consider both the maximum likelihood estimation and
Bayesian inference. We establish that the rate of convergence is linear an
d present tight bounds on the rate of convergence. The MM algorithm is sho
wn to have essentially the same convergence rate as the gradient descent a
lgorithm. For the maximum likelihood estimation\, the key parameter that d
etermines the convergence rate is the algebraic connectivity of a matrix w
hose elements are the counts of paired comparisons between distinct pairs
of items. We show that both gradient descent and MM algorithms can be arbi
trarily slow for Bayesian inference depending on the parameters of the pri
or distribution (we show this for a common prior used in practice). We the
n derive new\, simple to implement\, accelerated iterative optimization me
thods that resolve the slow convergence issue.
URL:https://www.imperial.ac.uk/events/97714/scalable-inference-for-statisti
cal-models-of-ranking-data/
DTSTART;TZID=Europe/London:20181218T130000
DTEND;TZID=Europe/London:20181218T140000
LOCATION:United Kingdom
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DTSTART:20181218T130000
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