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Bayesian elastic net regression
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Description
Rating
DOI number
10.14457/TU.the.2014.9
Title
Bayesian
elastic
net
regression
Creator
Kanyalin Jiratchayut
Creator in other language
กัญลิน จิรัฐชยุต
Subject
Elasticity
Regression analysis
Bayesian statistical decision theory
Keyword
Elasticity
Regression analysis
Bayesian statistical decision theory
Adaptive elastic net
Adaptive weight
Bayes factor
Bayesian analysis
Abstract
We
propose
the
method
for
estimating
the
value
of the
L2
penalty
parameter
,
λ_2
, of
elastic
net
linear
regression
model
using
Bayesian
analysis
. The
value
of
λ_2
is
specified
through
Bayes
factor
.
We
compare
the
performance
of the
value
of
λ_2
based
on
Bayes
factor
to the
value
of
λ_2
chosen
by
10fold
crossvalidation
method
.
Simulation
studies
and
real
data
examples
show
that the
value
of
λ_2
based
on
Bayes
factor
performs
better
in
prediction
accuracy
. The
value
of
λ_2
based
on
Bayes
factor
can
be
used
for
adaptive
elastic
net
estimator
where
the
adaptive
weight
is
included
in the
L1
penalty
.
We
study
the
performance
of
two
adaptive
elastic
net
estimation
methods
where
the
adaptive
weights
are
constructed
using
elastic
net
and
least
squares
estimators
.
Simulation
studies
show
that
two
adaptive
weights
perform
differently
.
When
the
elastic
net
estimator
is
used
, the
adaptive
elastic
net
performs
best
in
estimation
accuracy
and
variable
selection
performance
. If the
least
squares
estimator
is
used
, the
adaptive
elastic
net
has the
prediction
performance
better
than
using
the
other
adaptive
weight
.
We
study
the
performance
of the
Bayesian
variable
selection
for
elastic
net
linear
regression
model
(BVS)
using
two
different
priors
: the
penalty
parameters
λ_1
and
λ_2
are
estimated
by the
10fold
crossvalidation
, and the
penalty
parameter
λ_2
is
based
on
Bayes
factor
. The
variable
selection
result
of
BVS
differs
from
elastic
net
. The
BVS
performs
both
variable
selection
and
group
selection
where
the
pair
of
predictors
which
are
highly
correlated
with the
response
variable
is
included
into the
optimal
model
whereas
some
pair
of
predictors
which
are
highly
correlated
with the
response
variable
is
excluded
from the
elastic
net
model
. The
BVS
is
more
parsimonious
than the
elastic
net
. For
BVS
method
, the
prior
for the
penalty
parameters
λ_1
and
λ_2
estimated
by the
10fold
crossvalidation
method
is
the
best
.
Publisher
Thammasat University
Contributors
Chinnapong Bumrungsup, advisor
Date of issued
2014
Type
Text
Format
application/pdf
Formatextent
xiii, 351 leaves
Identifier (Full Text)
http://ethesisarchive.library.tu.ac.th/thesis/2014/TU_2014_5309320025_992_219.pdf
Language
eng
Rights
Copyright of Thammasat University. Licensed under a Creative Commons AttributionNonCommercialNoDerivatives license.
Rights holder
Thammasat University
Degree name
Doctor of Philosophy (Statistics)
Degree discipline
Statistics
Faculty/College
Faculty of Science and Technology
Description
Best
Dissertation
2014
(Third
Prize)
in
Science
and
Technology
CONTENTdm number
33933
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