uncertainty ai

8/18/2019 Uncertainty AI

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Paula MatuszekCSC 8520, Fall, 2005

I have already createdDealing with ncertainty

hahaha


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!rti"icial Intellignce, Fall 2005, Paula Matuszek

#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t 2

Intr%ducti%n

he w%rld is n%t a well)de"ined $lace&here is uncertainty in the "acts we kn%w3

hat4s the te-$erature I-$recise -easures

Is #ush a g%%d $resident I-$recise de"initi%nshere is the $it I-$recise kn%wledge

here is uncertainty in %ur in"erencesI" I have a .listery, itchy rash and was gardening allweekend I $r%.a.ly have $%is%n ivy

Pe%$le -ake success"ul decisi%ns all the ti-eanyh%w&


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S%urces %" ncertaintyncertain data

-issing data, unrelia.le, a-.igu%us, i-$recise re$resentati%n,inc%nsistent, su.7ective, derived "r%- de"aults, n%isy

ncertain kn%wledgeMulti$le causes lead t% -ulti$le e""ectsInc%-$lete kn%wledge %" causality in the d%-ainPr%.a.ilistic'st%chastic e""ects

ncertain kn%wledge re$resentati%nrestricted -%del %" the real syste-li-ited e9$ressiveness %" the re$resentati%n -echanis-

in"erence $r%cessDerived result is "%r-ally c%rrect, .ut wr%ng in the real w%rld:ew c%nclusi%ns are n%t well)"%unded ;eg, inductive reas%ning<Inc%-$lete, de"ault reas%ning -eth%ds


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=eas%ning nder ncertainty

S% h%w d% we d% reas%ning under uncertaintyand with ine9act kn%wledgeheuristics

ways t% -i-ic heuristic kn%wledge $r%cessing -eth%ds

used .y e9$ertse-$irical ass%ciati%ns

e9$eriential reas%ning.ased %n li-ited %.servati%ns

$r%.a.ilities%.7ective ;"re>uency c%unting<su.7ective ;hu-an e9$erience


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Decisi%n -aking with uncertainty

Rational .ehavi%r3F%r each $%ssi.le acti%n, identi"y the $%ssi.le%utc%-esC%-$ute the probability %" each %utc%-e

C%-$ute the utility %" each %utc%-eC%-$ute the $r%.a.ility)weighted (expected) utility %ver $%ssi.le %utc%-es "%r each acti%nSelect the acti%n with the highest e9$ected utility;$rinci$le %" Maximum Expected Utility


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S%-e =elevant Fact%rs

e9$ressivenesscan c%nce$ts used .y hu-ans .e re$resented ade>uatelycan the c%n"idence %" e9$erts in their decisi%ns .e e9$ressed

c%-$rehensi.ilityre$resentati%n %" uncertainty

utilizati%n in reas%ning -eth%dsc%rrectness

$r%.a.ilitiesrelevance rankingl%ng in"erence chains

c%-$utati%nal c%-$le9ity"easi.ility %" calculati%ns "%r $ractical $ur$%ses

re$r%duci.ilitywill %.servati%ns deliver the sa-e results when re$eated


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#asics %" Pr%.a.ility he%ry-athe-atical a$$r%ach "%r $r%cessing uncertain in"%r-ati%n

sa-$le s$ace set? @ A9+, 92, , 9nB

c%llecti%n %" all $%ssi.le eventscan .e discrete %r c%ntinu%us

$r%.a.ility nu-.er P;9i


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C%-$%und Pr%.a.ilities

descri.es independent eventsd% n%t a""ect each %ther in any way

joint $r%.a.ility %" tw% inde$endent events ! and #P;! ∩ #< @ P;!< E P ;#<

union $r%.a.ility %" tw% inde$endent events ! and#P;! ∪ #< @ P;!< P;#< ) P;! ∩ #<

@P;!< P;#< ) P;!< E P ;#<


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Pr%.a.ility the%ryRandom variables

D%-ain

Atomic event 3 c%-$letes$eci"icati%n %" state

Prior probability 3 degree%" .elie" with%ut any %therevidenceJoint probability 3 -atri9%" c%-.ined $r%.a.ilities%" a set %" varia.les

!lar-, #urglary, Harth>uake#%%lean ;like theseuake@Falsealar- ∧ .urglary ∧ earth>uake

P;#urglary< @ &+

P;!lar-, #urglary< @alar- alar-

.urglary &0G &0+

.urglary &+ &8


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Pr%.a.ility the%ry ;c%nt&<Conditional probability 3$r%.a.ility %" e""ect givencausesComputing conditionalprobs 3

P;a J .< @ P;a ∧ .< ' P;.<P;.


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Inde$endencehen tw% sets %" $r%$%siti%ns d% n%t a""ect each %thers4

$r%.a.ilities, we call the- independent , and can easily c%-$utetheir 7%int and c%nditi%nal $r%.a.ility3

Inde$endent ;!, #< i" P;! ∧ #< @ P;!< P;#


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H9ercise3 Inde$endence

ueries!

"s smart independent o# study $"s prepared independent o# study $

p(smartstudy

prep)

smart smartstudy study study study

prepared &*62 &+/ &08* &008

prepared &0*8 &+/ &06/ &0 2


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C%nditi%nal inde$endence

!.s%lute inde$endence3 ! and # are independent i" P;! ∧ #< @ P;!< P;#<e>uivalently, P;!< @ P;! J #< and P;#< @ P;# J !<

! and # are conditionally independent given C i" P;! ∧ # J C< @ P;! J C< P;# J C<

his lets us dec%-$%se the 7%int distri.uti%n3P;! ∧ # ∧ C< @ P;! J C< P;# J C< P;C<

M%%n)Phase and #urglary are conditionallyindependent given Night)Nevel

C%nditi%nal inde$endence is weaker than a.s%luteinde$endence, .ut still use"ul in dec%-$%sing the "ull

7%int $r%.a.ility distri.uti%n


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H9ercise3 C%nditi%nal inde$endence

ueries!"s smart conditionally independent o#

prepared % given study $"s study conditionally independent o#

prepared % given smart $

p(smartstudy prep)

smart smart

study study study study

prepared &*62 &+/ &08* &008

prepared &0*8 &+/ &06/ &0 2


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C%nditi%nal Pr%.a.ilities

descri.es dependent eventsa""ect each %ther in s%-e way

conditional probability %" event a given that event# has already %ccurredP;!J#< @ P;! ∩ #< ' P;#<


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#ayesian !$$r%aches

derive the $r%.a.ility %" an event given an%ther eventL"ten use"ul "%r diagn%sis3

I" ? are ;%.served< e""ects and O are ;hidden< causes,e -ay have a -%del "%r h%w causes lead t% e""ects ;P;? J Ouency %" %ccurrence %" e""ects ;P;O


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#ayes4 =ule "%r Single Hvent

single hy$%thesis , single event HP; JH< @ ;P;HJ < E P;


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#ayes H9a-$le3 Diagn%sing Meningitis

Su$$%se we kn%w thatSti"" neck is a sy-$t%- in 50Q %" -eningitis casesMeningitis ;-< %ccurs in +'50,000 $atientsSti"" neck ;s< %ccurs in +'20 $atients

henP;sJ-< @ 0&5, P;-< @ +'50000, P;s< @ +'20P;-Js< @ ;P;sJ-< P;-


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!dvantages and Pr%.le-s L" #ayesian

=eas%ningadvantagess%und the%retical "%undati%nwell)de"ined se-antics "%r decisi%n -aking

$r%.le-sre>uires large a-%unts %" $r%.a.ility data

su""icient sa-$le sizessu.7ective evidence -ay n%t .e relia.leinde$endence %" evidences assu-$ti%n %"ten n%t valid

relati%nshi$ .etween hy$%thesis and evidence is reduced t% anu-.er e9$lanati%ns "%r the user di""iculthigh c%-$utati%nal %verhead


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S%-e Issues with Pr%.a.ilities

L"ten d%nRt have the dataust d%nRt have en%ugh %.servati%nsData canRt readily .e reduced t% nu-.ers %r "re>uencies&

u-an esti-ates %" $r%.a.ilities are n%t%ri%uslyinaccurate& In $articular, %"ten add u$ t% T+&D%esnRt always -atch hu-an reas%ning well&

P;9< @ + ) P;)9


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De-$ster)Sha"er he%ry

-athe-atical the%ry %" evidence:%tati%ns

Hnvir%n-ent 3 set %" %.7ects that are %" interestframe of discernment FD

$%wer set %" the set %" $%ssi.le ele-ents

-ass $r%.a.ility "uncti%n -assigns a value "r%- 0,+ t% every ite- in the "ra-e %"discern-ent

mass probability -;!<$%rti%n %" the t%tal -ass $r%.a.ility that is assigned t%an ele-ent ! %" FD


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D)S nderlying c%nce$t

he -%st .asic $r%.le- with uncertainty is %"ten with thea9i%- that P;?< P;n%t ?< @ +I" the $r%.a.ility that y%u have $%is%n ivy when y%u have arash is &6, this -eans that a rash is str%ngly suggestive ;& <that y%u d%n4t have $%is%n ivy&

rue, in a sense, .ut neither intuitive n%r hel$"ul&

hat y%u really -ean is that the $r%.a.ility is &6 that y%uhave $%is%n ivy and & that we don’t know yet what y%uhave&

S% we initially assign all %" the $r%.a.ility t% the t%tal set%" things y%u might have3 the "ra-e %" discern-ent&


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Hnvir%n-ent3 Mentally retarded ;M=


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t

2*

Fra-e %" Discern-ent3

Mentally retarded ;M=


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2G

Inter$retati%n3 S%-e Hvidential

IntervalsC%-$letely true3 +,+C%-$letely "alse3 0,0C%-$letely ign%rant3 0,+

D%u.t )) dis.elie" in ?3 D.t @ #el; n%t ?<Ign%rance )) range %" uncertainty3 Igr @Pls)#el

ends t% su$$%rt3 #el, + ;0W#elW+<ends t% re"ute3 0, Pls ;0TPlsW+<

ends t% .%th su$$%rt and re"ute3 #el, Pls;0W#elWPlsW+<


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60

!dvantages and Pr%.le-s %"

De-$ster)Sha"er advantagesclear, rig%r%us "%undati%na.ility t% e9$ress c%n"idence thr%ugh intervals

certainty a.%ut certainty

$r%.le-sn%n)intuitive deter-inati%n %" -ass $r%.a.ilityvery high c%-$utati%nal %verhead

-ay $r%duce c%unterintuitive results due t%n%r-alizati%n when $r%.a.ilities are c%-.inedStill hard t% get nu-.ers


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t 6+

Certainty Fact%rs

shares s%-e "%undati%ns with De-$ster)Sha"erthe%ry, .ut -%re $racticalden%tes the .elie" in a hy$%thesis given thats%-e $ieces %" evidence are %.servedno statements a.%ut the .elie" is no evidence is

present in c%ntrast t% #ayes4 -eth%d


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#elie" and Dis.elie"

-easure %" .elie" degree t% which hy$%thesis is su$$%rted .yevidence HM#; ,H< @ + IF P; < @+

;P; JH< ) P;


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Certainty Fact%r

certainty "act%r CFranges .etween )+ ;denial %" the hy$%thesis < and+ ;c%n"ir-ati%n %" <

CF @ ;M# ) MD< ' ;+ ) -in ;MD, M#


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t 6*

C%-.ining Certainty Fact%rs

certainty "act%rs that su$$%rt the sa-e c%nclusi%nseveral rules can lead t% the sa-e c%nclusi%na$$lied incre-entally as new evidence .ec%-esavaila.le

C"rev;CF%ld, CFnew< @CF%ld CFnew;+ ) CF%ld< i" .%th T 0CF%ld CFnew;+ CF%ld< i" .%th W 0CF%ld CFnew ' ;+ ) -in;JCF%ldJ, JCFnewJ


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!dvantages %" Certainty Fact%rs

!dvantagessi-$le i-$le-entati%nreas%na.le -%deling %" hu-an e9$erts4 .elie"

e9$ressi%n %" .elie" and dis.elie" success"ul a$$licati%ns "%r certain $r%.le-classesevidence relatively easy t% gather

n% statistical .ase re>uired


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t 6/

Pr%.le-s %" Certainty Fact%rs

Pr%.le-s$artially ad h%c a$$r%ach

the%retical "%undati%n thr%ugh De-$ster)Sha"erthe%ry was devel%$ed later

c%-.inati%n %" n%n)inde$endent evidenceunsatis"act%rynew kn%wledge -ay re>uire changes in the certainty"act%rs %" e9isting kn%wledgecertainty "act%rs can .ec%-e the %$$%site %"c%nditi%nal $r%.a.ilities "%r certain casesn%t suita.le "%r l%ng in"erence chains


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Fuzzy N%gic

a$$r%ach t% a "%r-al treat-ent %" uncertaintyrelies %n >uanti"ying and reas%ning thr%ughnatural ;%r at least n%n)-athe-atical< language=e7ects the underlying c%nce$t %" an e9cluded-iddle3 things have a degree %" -e-.ershi$ in ac%nce$t %r set

!re y%u tall !re y%u rich

!s l%ng as we have a way t% "%r-ally descri.edegree %" -e-.ershi$ and a way t% c%-.inedegrees %" -e-.ershi$s, we can reas%n&


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Fuzzy Setcateg%rizati%n %" ele-ents 9i int% a set S

descri.ed thr%ugh a -e-.ershi$ "uncti%n -;s<ass%ciates each ele-ent 9i with a degree %"-e-.ershi$ in S

$%ssi.ility -easure P%ssA9 ∈ SBdegree t% which an individual ele-ent 9 is a $%tential-e-.er in the "uzzy set Sc%-.inati%n %" -ulti$le $re-ises

P%ss;! ∧ #< @ -in;P%ss;!


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Fuzzy Set H9a-$lemembership

height (cm)0

050 100 150 200 250

0.5

1 short medium tall


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t *0

Fuzzy vs& Cris$ Setmembership

height (cm)0

050 100 150 200 250

0.5

1 short medium tall


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t *+

Fuzzy =eas%ning

In %rder t% i-$le-ent a "uzzy reas%ning syste-y%u needF%r each varia.le, a de"ined set %" values "%r-e-.ershi$

Can .e nu-eric ;+ t% +0<Can .e linguistic

really n%, n%, -ay.e, yes, really yestiny, s-all, -ediu-, large, gigantic

g%%d, %kay, .ad !nd y%u need a set %" rules "%r c%-.ining the-

X%%d and .ad @ %kay&


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Fuzzy In"erence Meth%ds

N%ts %" ways t% c%-.ine evidence acr%ss rulesP%ss;#J!< @ -in;+, ;+ ) P%ss;!< P%ss;#


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S%-e !dditi%nal Fuzzy C%nce$ts

Su$$%rt set3 all ele-ents with -e-.ershi$ T 0 !l$ha)cut set3 all ele-ents with -e-.ershi$greater than al$ha

eight3 -a9i-u- grade %" -e-.ershi$:%r-alized3 height @ +

S%-e ty$ical d%-ainsC%ntr%l ;su.ways, ca-era "%cus<Pattern =ec%gniti%n ;LC=, vide% sta.ilizati%n<In"erence ;diagn%sis, $lanning, :NP<


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!rti"icial Intellignce, Fall 2005, Paula Matuszek#ased in $art %n www&csc&cal$%ly&edu'("kur"ess'C%urses'CSC)*8+' 02'Slides' ncertainty&$$t and www&cs&u-.c&edu'c%urses'graduate'/ +'"all05'slides'c+81$r%.&$$t **

!dvantages and Pr%.le-s %" Fuzzy

N%gicadvantagesgeneral the%ry %" uncertaintywide a$$lica.ility, -any $ractical a$$licati%ns

natural use %" vague and i-$recise c%nce$tshel$"ul "%r c%--%nsense reas%ning, e9$lanati%n

$r%.le-s-e-.ershi$ "uncti%ns can .e di""icult t% "ind-ulti$le ways "%r c%-.ining evidence$r%.le-s with l%ng in"erence chains


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ncertainty3 C%nclusi%nsIn !I we -ust %"ten re$resent and reas%n a.%ut uncertainin"%r-ati%n

his is n% di""erent "r%- what $e%$le d% all the ti-eUhere are -ulti$le a$$r%aches t% handling uncertainty&

Pr%.a.ilistic -eth%ds are -%st rig%r%us .ut %"ten hard t%

a$$ly #ayesian reas%ning and De-$ster)Sha"er e9tend itt% handle $r%.le-s %" inde$endence and ign%rance %" dataFuzzy l%gic $r%vides an alternate a$$r%ach which .ettersu$$%rts ill)de"ined %r n%n)nu-eric d%-ains&

H-$irically, it is %"ten the case that the -ain need is s%-eway %" e9$ressing Y-ay.eY& !ny syste- which $r%vides "%rat least a three)valued l%gic tends t% yield the sa-edecisi%ns&

uncertainty ai

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