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!"#$%$&'&()&*+,"%-.&*%'+/#01'(+234-5)+6789: - - PDF document

Jun 15, 2023 225 likes •535 views

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\1()+Q#"+&<01-1<01<*&1(: /%"T#U+&<01-1<01<*1+ !%&"?&(1+&<01-1<01<*1 @>\C+)1()&<=+/%"T#U+#"+-%&"?&(1+&<U#'U1(+%''+U%"&%$'1(

LZ+1V-#<1<)&%'+&<+<54N+<#01( (11+<1V)+('&01

B[

\1()&<=+Q#"+&<01-1<01<*&1( S<01-1<01<*1+)1()&<=+5(&<=+-%&"?&(1+&<01-1<01<*1: P5--#(1+w+$&<%"X+<#01(: +++++++++++++(1)(+AdCeE+)#+)1() Q#"+1%*.+#Q+B+%((&=<41<)(+AVCXEC+45()+*.1*T+1Y5%'&)X+ 5<01"+G2wLG9+%((&=<41<)(+)#+#).1"+<#01(+&< LZ+1V-#<1<)&%'i 2(&4&'%"+%"=541<)+Q#"+/%"T#U+&<01-1<01<*19

BB

∃ N 2

  • X − {X, Y }

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-23
SLIDE 23

S<01-1<01<*1+)1()&<=+2KM+8ONDN89

2^((54&<=+01="11+24%V+€+10=1(+F+<#019+um+•+0m+••+w9

3#<(&01"+dCe

<#+10=1+LZ+++++++++++++++++%<0+++++++++++++++++(1-%"%)1+d+%<0+e

&N1N+∃+(1)+x+?&).+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ (5*.+).%)

(#:++ M#"+1%*.+-%&"+dCe+)1()+Q#"+10=1+5(&<=++++++++++++++++++++++)1()(

!#'X<#4&%'+<54$1"+#Q+)1()(

f%*.+)1()+&<U#'U1(+•+0mtG+U%"&%$'1(

  • +G0mtG+%((&=<41<)(+)#+*.1*T+Q#"+$&<%"X+<#01(+

\"%*)%$'1+Q#"+(4%''+0m

B7

3#<()"%&<)L$%(10+()"5*)5"1+'1%"<&<=+2KM+8ONDN89 ;&4&)%)&#<(:

%((541+um+-1"Q1*)+4%-+Q#"+!m %((541+$#5<010+#"01"+Q#"+um %((541+1<#5=.+0%)%+Q#"+"1'&%$'1+&<01-1<01<*1+)1()(

B6

d e x d e x !m 3#""1*)+um+5<"1%*.%$'1 $1*%5(1+d⊥e|AE

LZ+0&(*%"0+dLe+10=1

&N1N+<#+/%"T#U+<1)+&(+

  • 1"Q1*)+4%-+Q#"+!m

fV%4-'1

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-24
SLIDE 24

3#<()"%&<)L$%(10+()"5*)5"1+'1%"<&<=+2KM+8ONDN89 ;&4&)%)&#<(+2*#<)r09: M#"+/%"T#U+<1)(C+='#$%'+&<01-1<01<*1+()"5*)5"1+<#)+ <1*1((%"&'X+5(1Q5'

1=:+Q5''X+*#<<1*)10+<1)?#"T+?&).+-%&"?&(1+-#)1<)&%'( LZ+*#4-'1V+*#<<1*)&U&)X+$5)+*#4-%*)+Q%*)#"&W%)&#<

*#<()"%&<)L$%(10+'1%"<&<=+0#1(+<#)+.1'-+Q&<0+Q%*)#"&W%)&#<

BD

P*#"1L$%(10+'1%"<&<=+2KM+8ONDNG9 uX-#).1(&(+(-%*1

  • '#=L'&<1%"+4#01'

^'(#:

  • $%(&*+="%-.+()"5*)5"1
  • Q%*)#"+="%-.

LZ+0&QQ1"1<)+'1U1'(+#Q+4#01'+}="%<5'%"&)X~

BI

structure? factor graph?

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-25
SLIDE 25

P*#"1L$%(10+'1%"<&<=+2KM+8ONDNG9 uX-#).1(&(+(-%*1

  • '#=L'&<1%"+4#01'
  • ,&U1<+(1)+#Q+Q1%)5"1(+‚C

01"&U1+4#01'+++++++Q"#4+Q1%)5"1( $X+(1))&<=+++++++++++++&Q+ 2^'(#C+#-)&4&W1+#).1"++++++9

  • P)"5*)5"1+&4-'&*&)+&<+++++

*#<<1*)+%''+

BO

structure? factor graph?

θi = 0 φi / ∈ Φ[M] θi X ∈ scope(φi), ∀φi ∈ Φ[M]

P*#"1+Q5<*)&#<+2%'(#+(11+KM+8ONDN[N89 '#=L'&T1'&.##0 ]U1"Q&))&<=+-"#$'14 +++++++++++++++++++++++++++++++++LZ

4#"1+1V-"1((&U1+4#01'+Q&)(+<#&(1+&<+R 45()+"1()"&*)+Q%*)#"(r+1V-"1((&U1<1((+#"+"1=5'%"&W1

7H

4#01' 0%)%

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-26
SLIDE 26

,"110X+/w+()"5*)5"1+'1%"<&<=+2%'(#+(11+KM+M&=N+8ON[9

78

\#)%'+Q1%)5"1+(1)+ S<&)&%'+Q1%)5"1+(1) %)+%''+)&41(: S)1"%)1+A ]-)&4&W1++++++++2-%"%41)1"+#-)&4&W%)&#<9

S)1"%)1+#U1"+4#0&Q&*%)&#<+#-1"%)#"(++++++)#+()"5*)5"1+A +++++++++*"1%)1(+++++++++++++++++++++++++++2(11+<1V)+('&019 +++++++c+&4-"#U141<)+&<+(*#"1+ E *.##(1+(1)+#Q+4#0&Q&*%)&#<(+++++++$%(10+#<

LZ+<1?+()"5*)5"1+ E+

Φ0 Ω θi = 0, ∀φi / ∈ Φ θΦ Φmod O O ˆ ∆O O ˆ ∆O Φ

P)"5*)5"1+4#0&Q&*%)&#<

7G

P)"5*)5"1+4#0&Q&*%)&#<+()1-(++++++: %00+F+"14#U1+(&<='1+10=1 2<#+0&"1*)&#<%'&)Xi9

O

\.1<+<110+(*#"1+Q#"+1%*.+4#0&Q&*%)&#<

2(11+$1'#?9+ ˆ ∆O

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-27
SLIDE 27

P)"5*)5"1+(*#"&<=+2%'(#+(11+KM+8ONDNBNG9 @%X1(+<1)(:

()"5*)5"1+(*#"1+1U%'5%)&#<+1%(X

*'#(10+Q#"4+%U%&'%$'1

(*#"1+01*#4-#(1(+$%(10+#<+()"5*)5"1

*.%<=1+)#+()"5*)5"1+*.%<=1(+#<'X+#<1+)1"4+&<+).1+(*#"1 *.%<=1(+)#+0&QQ1"1<)+-%")(+#Q+()"5*)5"1+0#+<#)+&<)1"%*)+&<+).1+(*#"1

LZ+1QQ&*&1<*X:+0X<%4&*+-"#="%44&<=C+*%*.&<=C+1)*N

7[

P)"5*)5"1+'1%"<&<=+-1"Q#"4%<*1+2%'(#+(11+KM+8ONDNBNG9 /%"T#U+<1)(:

()"5*)5"1+(*#"1+1U%'5%)&#<+/"#4%#

7B

P*#"1+Q#"+1%*.+4#0&Q&*%)&#<+ 45()+#-)&4&W1

"1Y5&"1(+&<Q1"1<*1(+&<(&01+="%0&1<)+%(*1<)+'##- *%<+()%")+Q"#4+++++++++++++++++++)#+(-110+).&<=(+5- ()&''+1V-1<(&U1+2k+&<(&01+#U1"%''+()"5*)5"1+&)1"%)&#<+'##-9+

3.1%-1":+"%<T+#"01"+++++++++2&<()1%0+#Q+Q5''+1U%'5%)&#<+9+

ˆ ∆O θΦmod θΦcurrent ˆ ∆O

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-28
SLIDE 28

P)"5*)5"1+'1%"<&<=+-1"Q#"4%<*1+2%'(#+(11+KM+8ONDNBNG9 /%"T#U+<1)(:+()"5*)5"1+(*#"1+1U%'5%)&#<+/"#4%#

  • %")&)&#<+Q5<*)&#<+*#5-'1(+1U1"X).&<=

*#4-5)&<=+'&T1'&.##0+(*#"1+"1Y5&"1(+&<Q1"1<*1 ()"5*)5"1+(*#"1+"1Y5&"1(+-%"%41)1"+1()&4%)&#<+2<#+*'#(10+Q#"49 ()"5*)5"1+(*#"1+0#1(+<#)+01*#4-#(1 LZ+1V-1<(&U1i

,##0+<1?(:

()"5*)5"1+'1%"<&<=+&(+*#<U1V+2?&).+Q5''X+#$(1"U10+0%)%9

()"5*)5"1+'1%"<&<=+4#"1+1V-1<(&U1+Q#"+/%"T#U+U(N+@%X1(

77

J1=5'%"&W%)&#<+k+()"5*)5"1+'1%"<&<=+2%'(#+(11+KM+8ONDN[NG9 @%X1(&%<+(*#"1

4%"=&<%'+'&T1'&.##0

%U1"%=1+$%(10+#<+-%"%41)1"+-"&#"

"1=5'%"&W1(+-%"%41)1"(

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2$1*%5(1+#Q+-%")&)&#<+Q5<*)&#<9 5(1+@S3+(*#"1+&<()1%0+2<1V)+('&019

76

'&T1'&.##0

  • "&#"

Cmput 651 - Learning Undirected Models {14,17}/11/2008

slide-29
SLIDE 29

J1=5'%"&W%)&#<+k+()"5*)5"1+'1%"<&<=+2%'(#+(11+KM+8ONDN[NG9

^(X4-)#)&*+%--"#V&4%)&#<+)#+4%"=&<%'+'&T1'&.##0 0&42/9+c+0&41<(&#<+#Q+4#01' 01="11(+#Q+Q"110#4 LZ+-1<%'&W1(+4#"1+*#4-'1V+4#01'(+2&N1N+4#"1+RN]NMN9

7D

]).1"+"1=5'%"&W%)&#<(+Q#"+()"5*)5"1+'1%"<&<=+2KM+8ONDNB9

7I

/^!+(*#"1 ;8+"1=5'%"&W%)&#<

Cmput 651 - Learning Undirected Models {14,17}/11/2008