importance sampling, sequential importance sampling and more
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Importance Sampling, Sequential Importance Sampling and more. CS-295 Spring 2008. Estimation. Function : An assignment of weights to a domain Summation Problems Ratio over sums. Example: Function over 3 variables. Specification: Function is a Product of smaller Functions. - PowerPoint PPT PresentationTRANSCRIPT
Importance Sampling, Sequential Importance Sampling and more.
CS-295Spring 2008
Estimation
Function : An assignment of weights to a domain
Summation Problems
Ratio over sums
Xx
xf )(
Yy
Xx
yg
xf
)(
)(
Example: Function over 3 variables
A B C Weight
0 0 0 0.3
0 0 1 0.4
0 1 0 0.6
0 0 1 0.5
1 0 0 0.1
1 1 1 0.9
1 1 0 0.4
1 1 1 0.5
Specification: Function is a Product of smaller Functions
X: A set over n variables fi(y), i=1 to m is a function over a
subset of X f(X) is the product of all functions
XyyfxxXfm
iin
1
1 )(}),..,{(
Distribution: A function whose weights sum to 1.
))(|()(
))(|( :CPTs
1ii
i
XpaXPXP
XpaXPn
i
i
lung Cancer
Smoking
X-ray
Bronchitis
Dyspnoea
Xx
xxh )()(
USE REJECTION SAMPLING
g(x)f(X)
Rejection Control
Given a constant c>0. For j=1 to m
Accept x(j) with probability r(j) = min {1,w(j)/c)
If x(j) is accepted update its weight as w(*j)=w(j)/r(j)
Let g*(x) be the sampling distribution, then:
)(
)(
)(*
)(
xg
xVar
xg
xVar