P(J '" M '" A '" ŹB '" ŹE)
= P(J|A)P(M|A)P(A|ŹB '" ŹE)P(ŹB)P(ŹE)
= 0.90 × 0.70 × 0.001 × 0.999 × 0.998 = 0.00062
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" Xi
P(Xi|Xi-1, . . . , X1) = P(Xi|P arents(Xi))
P arents(Xi) Ä…" {Xi-1, . . . , X1}
" {Xi}
" {Xi}
" {Xi}
Xi
P arents(Xi)
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JohnCalls
P(Burglary|JohnCalls) = 0.016
"
Burglary
P(JohnCalls|Burglary) = 0.86
P(MaryCalls|Burglary) = 0.67
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Alarm P(Burglary|Alarm) = 0.376
Earthquake
P(Burglary|Alarm '" Earthquake) = 0.003
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JohnCalls = T rue Eartquake = F alse
P(Alarm|JohnCalls '" ŹEartquake) = 0.03
P(Burglary|JohnCalls '" ŹEartquake) = 0.0017
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P(C)=0.5
P(C)=0.5
Cloudy
Cloudy
Cloudy
C P(S)
C P(S)
C P(S)
C P(R)
C P(R)
C P(R)
Sprinkler Rain
Sprinkler Rain
Sprinkler Rain
T 0.10
T 0.10
T 0.10
T 0.80
T 0.80
T 0.80
F 0.50
F 0.50
F 0.50
F 0.20
F 0.20
F 0.20
Wet grass
Wet grass
Wet grass
S R P(W)
S R P(W)
S R
S R P(W)
T T
T T 0.99
T T 0.99
T T 0.99
T F
T F 0.90
T F 0.90
T F 0.90
F T 0.90
F T 0.90
F T
F T 0.90
F F 0.00
F F 0.00
F F 0.00
F F
P(C)=0.5
P(C)=0.5
Cloudy
Cloudy
P(S+R=x)
P(S+R=x)
P(S+R=x)
C TT TF FT FF
C TT TF FT FF
C TT TF FT FF
T .08 .02 .72 .18
T .08 .02 .72 .18
T .08 .02 .72 .18
Spr+Rain
Spr+Rain
F .40 .10 .40 .10
F .40 .10 .40 .10
F .40 .10 .40 .10
S+ R P(W)
S+ R
S+ R P(W)
S+ R P(W)
T T
T T 0.99
T T 0.99
T T 0.99
Wet grass
Wet grass
T F 0.90
T F 0.90
T F
T F 0.90
F T
F T 0.90
F T 0.90
F T 0.90
F F
F F 0.00
F F 0.00
F F 0.00
+Cloudy +Cloudy -Cloudy -Cloudy
+Cloudy +Cloudy -Cloudy -Cloudy
+Cloudy +Cloudy -Cloudy -Cloudy
Sprinkler Rain Sprinkler Rain
Sprinkler Rain Sprinkler Rain
Sprinkler Rain Sprinkler Rain
Wet grass Wet grass
Wet grass Wet grass
Wet grass Wet grass
P(X|E)
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P(X|E) H" N(X '" E)/N(E)
N
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" Bel(X)
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1
(A)
0
100 140 180 220 260
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T(A) = A
" T ( )
T(A '" B) = min{T(A), T(B)}
T(A (" B) = max{T(A), T(B)}
T(ŹA) = 1 - T(A)
" T(A (" ŹA) = T(T rue)

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H
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H
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p n
p n p p n n
I( , ) = - log2 - log2
p + n p + n p + n p + n p + n p + n
" A
½

pi + ni pi ni
P ozostalo(A) = I( , )
p + n pi + ni pi + ni
i=1
A E E1, . . . , E½ pi, ni
"
p n
Gain(A) = I( , ) - P ozostalo(A)
p + n p + n
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" X
" D
" H
" f " H
h " H
" m
" h " H f
error(h) = P{h(x) = f(x) | x wylosowane z D}

"
µ
error(h) d" µ
" ´

1 1
m e" ln + ln |H|
µ ´
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