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CATEGORIES:Machine Learning @ CUED
SUMMARY:Shrinkage regression for multivariate inference wi
th missing data\, with an application to portfol
io balancing - Robert B. Gramacy (University of Ca
mbridge)
DTSTART;TZID=Europe/London:20090310T150000
DTEND;TZID=Europe/London:20090310T160000
UID:TALK16871AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16871
DESCRIPTION:Asset return histories can greatly vary in length.
Such data are said to follow a monotone missingne
ss pattern\, which leads to a convenient factoriza
tion of the likelihood for the purposes of inferen
ce. Under an MVN assumption\, MLEs and samples fro
m a Bayesian posterior can be obtained by repeated
OLS regression\, one for each asset. When there a
re more assets than historical returns (a "big p s
mall n problem")\, however\, OLS becomes unstable.
We explore remedies that apply shrinkage\, like r
idge regression or the lasso\, which have a natura
l Bayesian implementation\, and can offer improvem
ents in accuracy and interpretation. We focus on t
he Bayesian approach and thus improve upon the wor
k of Stambaugh (1997) to provide full posterior in
ference rather than just moments\, in addition to
extending its reach to the "big p small n" setting
. We show how\, in this framework\, it is straigh
tforward to relax the MVN and monotonicity assumpt
ions\, incorporate known factors\, test hypotheses
about correlation\, obtain credible intervals all
parameters in the model and\, in particular\, obt
ain uncertainty bands for the solutions to the qua
dratic programs using samples from the posterior t
o\, e.g.\, balance portfolios. Where possible\, we
provide detailed comparisons to the alternative M
L approach. We conclude with an investment exerci
se and descriptive analysis based on real financia
l returns data. An R package implementing all of
the methods described herein is available on CRAN.
\n
LOCATION:Engineering Department\, CBL Room 438
CONTACT:Zoubin Ghahramani
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