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SUMMARY:Improved Nonparametric Empirical Bayes Estimation using Transfer L
 earning - Gourab Mukherjee\, University of Southern California
DTSTART:20200522T130000Z
DTEND:20200522T140000Z
UID:TALK140257@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We consider the problem of estimating a multivariate normal me
 an in the presence of possibly useful auxiliary variables. The traditional
  nonparametric empirical Bayes (NEB) framework provides an elegant interfa
 ce to pool information across dimensions and facilitates the construction 
 of effective shrinkage estimators. Such estimators can be further improved
  by incorporating pertinent information from the auxiliary variables. Howe
 ver\, detecting and assimilating possibly useful information from auxiliar
 y variables to shrinkage estimators is difficult. Here\, we develop a new 
 methodology that can transfer useful information from multiple auxiliary v
 ariables and yield improved Tweedie-type NEB estimators. Our method uses c
 onvex optimization to directly estimate the gradient of the log-density th
 rough an embedding in the reproducing kernel Hilbert space induced by the 
 Stein's discrepancy metric. We establish asymptotic optimality of the resu
 ltant estimator. We precisely tabulate the improvements in the estimation 
 error as well as the deterioration in the learning rate as we inspect an i
 ncreasing number of auxiliary variables. We demonstrate the competitive op
 timality of our method over existing NEB approaches through simulation exp
 eriments and in real data settings. This is joint work with Jiajun Luo and
  Wenguang Sun.      
LOCATION: https://zoom.us/j/95022384263?pwd=N3Z6elB2Vy9Jajd6azlCNjFHQVlKdz
 09
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