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Daphne Koller
U"lity Func"ons
Probabilis"c Graphical Models Decision Making
Ac"ng
Utilities and Preferencesf
0.2 $4mil 0.25 $3milf
p
0.8 $0 0.75 $0≈
Daphne Koller
Utility = Payoff?y y ff
0.8 $4mil 1 $3milf
p
0.2 $0 0 $0≈
Daphne Koller
St. Petersburg Paradox• Fair coin is tossed repeatedly until it
gp y
comes up heads, say on the nth toss• Payoff = $2n• Payoff = $2n
Daphne Koller
UU($500)
UD
U($500)D=
$0 with prob. 1-p
$1000 with prob pUD $1000 with prob. p
$ reward10000 500400
C t i t i l t
Daphne Koller
Certainty equivalent insurance/risk premium
Typical Utility CurveU
yp yU
$
Daphne Koller
Multi-Attribute Utilities• All attributes affecting preferences must g p
be integrated into one utility function
H l f• Human life– Micromorts
Daphne Koller
– QALY (quality-adjusted life year)
Example: Prenatal diagnosismp gU1(T) + U2(K) + U3(D,L) + U4(L,F)
Testing Knowledgeg g
f’ Loss offetus
Futurepregnancy
Down’ssyndrome
Daphne Koller
Summarymm y• Our utility function determines our preferences
b t d isi s th t i l t i tabout decisions that involve uncertainty• Utility generally depends on multiple factors
M ti h f d th – Money, time, chances of death, …• Relationship is usually nonlinear
Sh f tilit d t i ttit d t i k– Shape of utility curve determines attitude to risk• Multi-attribute utilities can help decompose
high dimensional function into tractable pieces
Daphne Koller
high-dimensional function into tractable pieces