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! "

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# $% &

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4

/ ; $ $ 2

/ ε 1 ! <δ

/ ) ! & $ $ ! Ĥ

/ = >& < Ĥ> ? ε>&> @ A <δ

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4

/ B ) 1 C

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B D E $

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B G ) 4 H

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E $

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E $

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4"%* 3 #2 ) ) # 0 ( 2 *) ) % % * 5 ) #% )6

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) #

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*), #%( # & 2" ( *) % < (

% % ); 3 #2 ))" <,) : ,

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%&&&&& %&&&&&&&& %&&&&&& '

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:(

posterior = likelihood ⇥ prior evidence

P (C|x) = P (x|C)P (C) P (x)

P (C|x) / Y

xi2x

P (xi|C)P (C)

C = arg max

C

P (C|x)

(37)

Attribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5

Output hw~(~xi) w1

w2

w3

w4

w5

/ M .

/ , E x !

/ N w x N σ w x

/ σ 4 N % O <4 σʹNσ 4 <σ 4

/ I K w N ! <ỹ

/ ;, wO N w < ηK x

/ K N < ! <ỹ ỹ <ỹ

/ wO N w O η ! <ỹ ỹ < x

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,

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* ) 2 P !

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9 ) 3> < ); #% ) !%"# ) ))" <,) 0 3@ ); *% ( #% ) !%"# ) %

% !!( ' <%, (. 2 ) ! 53>6 : 53@6 A ε =

rR2 ln(1/δ) 2n

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2 * ! ) $ 4

* ) 1 ) !

!NR 4

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4

/ G

/ $ !

E ! E%% !H

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Attribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5

Output hw~(~xi) w1

w2

w3

w4

w5 / M

/ , E x !

/ N w x N w x

/ I K w N ! <

/ ;, wS N w < ηK x

/ K N < ! <

/ wS N w O η ! < x

"

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9

/ ) ) $

/ $ N * * ) 


$ 2 * P !

/ ; N $) $ $ $ * * !

":

σ =

qX

( ˜yi − yi)2/(N − 1)

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9)

/ E * ! $

* 4 4 $

$ ) $ $

/ 9) E 2< $ $)

$ * ) *

/ G )2. E

/ G $

/ 4 $ )

/ $ $

""

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E.g: x = [4,1,1,2]

ˆf (x) = X

Rl2S(xi)

lyˆl,

$ * $ 9)

/ 9) E 2 )

/ 9) $ E $

/ 9) $

/ B $ * H 2 $ 2 )

* 4

/ B * !

/ , 2 ) ) * ) * $

"'

H $ #H KH ; H T $ * $ 9) 2 , HT # M< D,, U :

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# , 2

"(

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, .

; * ) V)

4 4 W 4 ) ) 2

$ ) $

$ 4̂ O I

>4̂ O 4 O >

"

) )

/ $

/ 2

E E%%111H H

(48)

xt -

Estimator

- Alarm-

Change Detector

Estimation-

Memory -

6

6?

/ # $

* ) 2 $

/ ) $ $

1 4

/ # $ ) 2

/ ) N 2 % !

)

/ $ < 22 1 $

) $ * $

2

"C

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#) ) * )

/ 1 2 ) $ $ 22 2 I

/ ! ) )

/ E $ $ 2 $ *

/ N N 4 < O ε < *

/ 2 A X N

"-

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Number of examples processed (time)

Error rate

concept drift

pmin + s

min

Drift level

Warning level

0 5000

0 0.8

new window

#

/ $ 1 $ 1

/ 0) ! E

1 1 $ 1

/ 2 A 1 *

1 $

) 1 $ 1

/ 2 A $ 2 *

) ) 1 $ 2 $

'

K ; H $ ;H # H 9 $ ) E YM 1 , 2 , ZH + S "

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# < $ 6 ,

/ $ 1 $ 1 $ 1

/ D )2. $

/ 9 G $ ! 2 & 22$

/ 2 2 1 ) $ 1 <

1 ) ! 2

/ ) $ O B !

/ ) 2

$ ) 2 ) 1 $ 1

'

;H &) MH H , E Y <# , ZH D,, U

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& 22$ $ *

/ 9 2 V) ! ) !

/ 0 $ 2 1 $ 1 2

/ )2. G ! !

/ <2 $ O 1

) 2 ) 1 ,B 0

/ D $ 1 $ 1 1 


Y < ! Z

'

H + 2 9H ; * $[E Y $ * <2 M 2 * * , Z , -

H + 2 9H ; * $[E YM 2 <# , 1 $ * B $ 1 ZH , U

(53)

,B 0

':

(54)

,B 0

'"

(55)

,B 0

''

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,B 0

'(

(57)

$ * 9 $

/ B ! 9 $ 3

/ 22< < 2

/ ; $ 2 9 $ )

; & X + 2 X 9 $ KX + $$ K X G X

2 +X & ;X $ H

M H

/ + $ 9 $ ! +

'

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$ * 9 $

H ) ) *

H 9 $ ! ) 2 2 ) 2

:H 8 & 22$

"H $ 2 $ 1 $

'H G ) $ 2 $$

(H ! $ $

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<G00

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<# )

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PE ) 2 V) $ * ) 2 $ H P

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/ ) < % ) <

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B J 4 3

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, #OO

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6

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+ ,

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;H , H + 2 E Y E $* $ * ! ZH K M9 "

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= =

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6

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D )

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