Anomaly Detection in KDD2019

Anomaly Detection in KDD2019

KDD2019読み会

67d58b26197110809c99b7ef43f8e0f6?s=128

Takahiro Yoshinaga

October 16, 2019
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  1. 0 D E B , 9 , 2 1@ 1@1

    / 1 /1 16 0 6 1 1
  2.   • _ h  01 • L 1

    • 6 S ü c • ü D N • i ü a I E ü e g 6
  3. • e v i r • c a ü P

    S I n n i i di K ,
  4. , , 4 :G: F F ü -C B :

    B B :A:B DDFC CF -C K F: CAAIB M : : CB ü :EI:B BCA M : : CB IG B B :FG: : B CF :A:B : FB B ü ::D BCA M : : CB K : CB : KCF G ü G C :F B B:LD: : C CB B: F B :F CBG B :B CL -C : G ü ( G B IF : BCA M : : CB B MB A )F D G K KC FCB : DDFC CG :F DD : :B : F ü A: :F :G BCA M : : CB :F : - FCGC ü BCA M : : CB CF B CAA:F : F B MG :A ü CB :L M FCLM :B M B CB :L I BCA :G G B B I DI FCLM CG :F ü : : B BCA :G B D : IG B -I F : CB C I CB - K - L IF:G C FC G CG :F ü C IG BCA M : : CB CF -I F : A: :F :G FCI C G : IFF:B :IF : KCF CG :F CF G CD CB BCA M : : CB B ( B B :
  5. 5 :F: E E ü -CG B : B B

    :A:BG DDEC CE -CG E: CAA B GL :G: G CB ü - ü ::D BCA L :G: G CB G :I G CB :G CE F ü F CI:E B B:KD: G: C CB B: E BG:E G CBF B :BG CK -C : F ü ( FG B E G: BCA L :G: G CB B LB A )E D F G C ECB : DDEC CFG:E DD : G :B : E ü - ü BCA L :G: G CB CE B CAA:E : E B LFG:A ü CBG:KG L ECKL :BG L B CBG:KG BCA :F F B B GD G ECKL CFG:E ü :G: G B BCA :F B D : F B - G I E G: CBIC G CB - G - KG E:F C EC FG CFG:E ü C FG BCA L :G: G CB CE - G I E G: A: :E :F G EC GC FG : EE:BG : E :G CE CFG:E CE F CD CB BCA L :G: G CB B ( B B :
  6. ::: . 2 . 9- : 1 - / 120

    / -21 -1 -19 -1 2 0 1 / 1-1
  7.    • 1 B ü )=1: = B

    B 1: 1B1 G ce • ,=B 1B = ü o m u o g a f M • - = = 1: ü tw RSB1 B da iI q k P L p s n ü b aG P • -= B ü 1 : 1 1   1 =  ü      1 = :     n v • :B ü )- b aT lr = 1:: ( = ü B1 BF P (- yT = 1F 1 tw + ==B B 1
  8. () 1 1 ( N L ==A A 1 1

    b Fdbe c J K M A = L 2 r (s, a) = 1 K K X k=1 (r✓k (s, a) ¯ r✓(s, a))2 <latexit sha1_base64="pqU3PFSYEt/dWvy83pXuiP/hL+c=">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</latexit> 1 B A1 A =: • 1 = lL hn w • 1 1 1 A hm o svT • ) 1 A pR p(✓|⌧) <latexit sha1_base64="JSwFveUnvnCQ2GwvHf4/o8PCdEY=">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</latexit> = 1: A = 2 1 n(s, a) = ¯ r✓(s, a) ¯ r ¯r <latexit sha1_base64="HHm6VJTbz+qXODjGZpRu2Wzb6jA=">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</latexit> =: dbe t J 1: = A Jy ki ac u J P Igr ✓MAP = arg max ✓ E ⌧⇠D[log p(⌧|✓) + log p(✓)] = arg max ✓ J(✓) <latexit sha1_base64="zuk3WZ8fSbJO161xMEm+hMQvhpI=">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</latexit>
  9. • ,1 UMK Gts jI-2 -2 5 L j ,

    • 0 = := D -2 5 P S 1 R :A: =pd I y( l ( a . ) ) ) o e uTl e o i Lc l n r o K D
  10.   • n i E tu p ü F

    d r c F v G • / Gx v ü foE / G AF s • fo hG : ü y / ü i a a e ü m G hE t l
  11. . 0 - 0 :/ /2 / 2 1 /

    :/ 2/ 9 2
  12. • , ü f P Ro R R c e

    E P N C E up ,3 P eE v • ) ,3 ü t iR N ,3 * ,3 * yu ü * (( e * (( • ) ü ) ( ü c eEP M C * * (( G * (( rGMS g N G n • * 3 ü ) 3 ,3 R R N ms G l ) R R R e d aR
  13.   D : D4 Sli • k a •

    n > L mf 4 D • >4 D 1, • deN2 : F F OUNS P 0 A > D A 4 : • IE - Pgo • / F > SD D A S • -4 : M D D > cbP p A E D D 4> D >
  14. ) ) r ) = e g r A (

    x = (¯ x + mean)(1 + var) · r + x <latexit sha1_base64="8OjkYJmm6hFiWZ+zOhmNSoa13N4=">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</latexit> 1 • c m ) i ü p S R tCO N? O : ü l y daK tS R n O ü ou s ou y da = : O K
  15.     F •    

    ü 1 , , 1 •     ü 3, 3, •    ü 1 3 3 C 1
  16.   • M ü ( S MR ü S

    v o l g Ra sO • ) ) t R r Fn SF ü ) MI NC R M O • ) e yM ü m r R c P F NC ü mr A u c FO R ) P p hfiF P ) S O
  17.   • 1 0 a T 5/ 5 5

    / e D T • 0 5 a Tt Wk ü 5 5 / W ü 5 / W • 0 1 m T cR c 1 po t S ü r b h A s 1 0 n y b li s