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CATEGORIES:Statistics
SUMMARY:Improved Nonparametric Empirical Bayes Estimation 
 using Transfer Learning - Gourab Mukherjee\, Unive
 rsity of Southern California
DTSTART;TZID=Europe/London:20200522T140000
DTEND;TZID=Europe/London:20200522T150000
UID:TALK140257AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/140257
DESCRIPTION:We consider the problem of estimating a multivaria
 te normal mean in the presence of possibly useful 
 auxiliary variables. The traditional nonparametric
  empirical Bayes (NEB) framework provides an elega
 nt interface to pool information across dimensions
  and facilitates the construction of effective shr
 inkage estimators. Such estimators can be further 
 improved by incorporating pertinent information fr
 om the auxiliary variables. However\, detecting an
 d assimilating possibly useful information from au
 xiliary variables to shrinkage estimators is diffi
 cult. Here\, we develop a new methodology that can
  transfer useful information from multiple auxilia
 ry variables and yield improved Tweedie-type NEB e
 stimators. Our method uses convex optimization to 
 directly estimate the gradient of the log-density 
 through an embedding in the reproducing kernel Hil
 bert space induced by the Stein's discrepancy metr
 ic. We establish asymptotic optimality of the resu
 ltant estimator. We precisely tabulate the improve
 ments in the estimation error as well as the deter
 ioration in the learning rate as we inspect an inc
 reasing number of auxiliary variables. We demonstr
 ate the competitive optimality of our method over 
 existing NEB approaches through simulation experim
 ents and in real data settings. This is joint work
  with Jiajun Luo and Wenguang Sun.      
LOCATION: https://zoom.us/j/95022384263?pwd=N3Z6elB2Vy9Jajd
 6azlCNjFHQVlKdz09
CONTACT:Dr Sergio Bacallado
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