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2 .

3 x x

4 2 t= 0: : x α ij β j O x2

5 u I = α x j ij i i= 0 y j = + exp( u ) j v J = β y j= 0 j j o = + exp( v )

6 0 0 e x p e x p J j I j ij i i o x β α = = = + +..

7 2 3 8 x x t 0 0 0,,,,.,, P = f( x, x2) r t = 0 < 0.5 Pr t = = 0.5 t 2 Pr

8 o<0.5 o 0.5 Ox (, x) x x 2-2 x, x 2

9 Ox (, x) x x 2-2

10 Ox (, x) x x 2-2

11 P = r + exp f( x, x ) { } 2 Pr f( x, x 2) = sin(2 π x ) + x x + sin(2 π x ) 2 2 t = t = 0 : P r < 0.5 t = : P r 0.5 x = 0.80, x = 0.43, 2 P r ( 0.80, 0.43) = + exp[ sin(2π 0.80) sin(2 π 0. 43)] = t=0

12 o = + J β j e x p I j = 0 + e x p α ij x i i = 0

13 x2 x No. x, x2 [0,] No x2 x No.

14 P = r + exp f( x, x ) { } 2 Pr f( x, x 2) = sin(2 π x ) + x x + sin(2 π x ) sin(2 π x ) + x sin(2 π x ) + sin(2 π x ) 2 t = t = 0 : P r < 0.5 t = : P r 0.5

15 P ( r x, ) x2 x 2 x

16 x2 x

17 t= 0: : x α ij β j O x2

18 O O,,. Over fitting,,,.

19 AIC (Akaike Information Criterion) ( X ˆ θ ( X) ) AIC= - 2ln L ; + 2 p EIC (Extended Information Criterion) ( ˆ ( )) * EIC=-2ln L X; θ X + 2C C *

20 X = X, X, X,, X, X, X { } { }, 2, 3,, 998, 999, 000 X = X X X X X X * * * * * * *,

21 ( * ˆ θ ( X * )) ln L X ; ( ˆ( * θ X )) ln L X; C L X ˆ X L X ˆ X B B * * { ( ( )) ( ( ))} * * ln b; θ b ln ; θ b b= {, } θ = α β B=200 ij j ( ˆ( )) * X θ X + C EIC= -2ln L ; 2

22 AICEIC AIC EIC (AIC) (EIC) AIC EIC () ()

23 AICEIC (EIC,AIC) AIC. (EIC,AIC) () AICEIC,. ()

24 EIC (%) (EIC) EIC ()

25 P ( r x, ) x2 x 2 P = r + exp f ( x, x ) { } 2 x f ( x, x ) = sin(2 πx) + xx + sin(2 πx ) 2 2 2

26 Ox (, x2) x 2 x

27 Ox (, x2) x x

28 Ox (, x2) x x

29 Ox (, x2) x x

30 Ox (, x2) x x

31 x, x2 [-,] P ( r x, ) x2 x 2 P = r + exp f ( x, x ) { } 2 x f( x, x ) = 0.3exp( x) cos(2 πx )

32 AIC= Ox (, x2) x 2 x

33 AIC=30.85 Ox (, x2) x 2 x

34 AIC=27.44 Ox (, x2) x 2 x

35 AIC=34.53 Ox (, x2) x 2 x

36 . Ox (, x) x x 2-2

37 x x

38 ,. No x2 x No x2 x No.

39 P ( r x, ) x2 x 2 P = r + exp f ( x, x ) { } 2 x f ( x, x ) = sin(2 πx) + xx + sin(2 πx ) 2 2 2

40 x2 x

41 EIC

42 ,

43 z = x 4.32x2 z < 0 z > 0, z = x 4.95x x x x x

44 z < 0 z > 0, z x 2 x z = x 4.32x 2

45 z < 0 z > 0, z x 2 x z = x 4.95x x x x x

46 P ( r x, ) x2 x 2 P = r + exp f ( x, x ) { } 2 x f ( x, x ) = sin(2 πx) + xx + sin(2 πx ) 2 2 2

47 x O x

48 Ox (, x2) x x 2 h=

49 ..

50 2 CART SupportVectorMachine (0.22) (0.259) 0.262

51 x 2 < 0.49 YES NO x < 0.57 x < 0.39 x No x x 2 < 0.3 x < 0.6 x 2 <

52 Support Vector Machine x x2 w w y SVM

53 ,. f ( x) y 2 y y 3 y n,. x x2 x3 xn

54 x x

55 2 CART SupportVectorMachine (0.22) (0.259)

58 g() x { f xθ ; θ Θ} ( )

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 = #A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/