.
x2.0 0.5 0 0.5.0 x
2 t= 0: : x α ij β j O x2
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 )
0 0 e x p e x p J j I j ij i i o x β α = = = + +..
2 3 8 x 75 58 28 36 x2 3 3 4 4 t 0 0 0,,,,.,, P = f( x, x2) r t = 0 < 0.5 Pr t = = 0.5 t 2 Pr
o<0.5 o 0.5 Ox (, x) 2 0.75 0.5 0.25 0 0-0 - x 2-3.86 0.204 x 2-2 x, x 2
Ox (, x) 2 0.75 0.5 0.25 0 0-0 - x 2-2.44 0.20 x 2-2
Ox (, x) 2 0.75 0.5 0.25 0 0-0 - x 2-20.37 0.20 x 2-2
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) 0.80 0.43 + sin(2 π 0. 43)] = 0.44 0.5t=0
o = + J β j e x p I j = 0 + e x p α ij x i i = 0
0.40 0.73 4 0.45 0.64 3 0.85 0.77 2 0.40 0.55 5 0.68 0.66 6 0.43 0.80 x2 x No. x, x2 [0,] No 0.23 0.44 996 0.99 0.49 995 0.3 0.50 997 0.4 0.98 998 0.22 0.50 000 0.34 0.90 999 x2 x No.
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 2 2 2 sin(2 π x ) + sin(2 π x ) 2 t = t = 0 : P r < 0.5 t = : P r 0.5
P ( r x, ) x2 x 2 x
x2 x
t= 0: : x α ij β j O x2
O O,,. Over fitting,,,.
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 *
X = X, X, X,, X, X, X { } 2 3 998 999 000 { }, 2, 3,, 998, 999, 000 X = X X X X X X * * * * * * *,
( * 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
AICEIC 2 3 4 5-48.82-339.62-40.59-9.72-6.24 AIC 973.65 697.25 307.9 73.43 74.47 EIC 978.72 697.90 303.94 64.25 66.0 (AIC) (EIC) AIC EIC () ()
AICEIC (EIC,AIC) AIC. (EIC,AIC) () AICEIC,. ()
2 3 4 5-48.82-339.62-40.59-9.72-6.24 EIC 978.72 697.90 303.94 64.25 66.0 0.220 0.47 0.055 0.003 0.002 (%) (EIC) EIC ()
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
Ox (, x2) x 2 x -48.82 0.220
Ox (, x2) x 2-339.62 0.47 x
Ox (, x2) x 2-40.59 0.055 x
Ox (, x2) x 2-9.72 0.003 x
Ox (, x2) x 2-6.24 0.002 x
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 ) + 0.3 2 2
AIC=607.45 Ox (, x2) x 2 x -298.72 0.58
AIC=30.85 Ox (, x2) x 2 x -6.42 0.003
AIC=27.44 Ox (, x2) x 2 x -0.72 0.000
AIC=34.53 Ox (, x2) x 2 x -0.26 0.000
. Ox (, x) 2 0.75 0.5 0.25 0 0-0 - x 2-2.44 0.20 x 2-2
x2.0 0.5 0 0.5.0 x
,. No 0.42 0.45 4 0.36 0.97 3 0.93 0.70 2 0.32 0.05 5 0.80 0.32 6 0.3 0.9 x2 x No. 0.5 0.82 996 0.09 0.45 995 0.6 0.94 997 0.4 0.30 998 0.86 0.70 000 0.57 0.64 999 x2 x No.
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
x2 x
2 3 4 5 0.220 0.47 0.055 0.003 0.002 0.264 0.70 0.064 0.02 0.00 EIC
2 0.003 0.02,
z = 4.33 3.82x 4.32x2 z < 0 z > 0, 0.234 0.266. z = 2.85 5.38x 4.95x + 5.04x + 3.26x x + 3.90x 2 2 2 2 2 0.22 0.259
z < 0 z > 0, z x 2 x z = 4.33 3.82x 4.32x 2
z < 0 z > 0, z x 2 x z = 2.85 5.38x 4.95x + 5.04x + 3.26x x + 3.90x 2 2 2 2 2
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
x O x2 0.220 0.262
Ox (, x2) x x 2 h= 0.220 0.220 0.264 0.262
..
2 CART SupportVectorMachine 0.003 0.234 (0.22) 0.220 0.02 0.266 (0.259) 0.262
x 2 < 0.49 YES NO x < 0.57 x < 0.39 x No x 2 438 0.78 0.37 2 x 2 < 0.3 x < 0.6 x 2 < 0.95 0.023 0.066
Support Vector Machine x x2 w w y SVM 0.053 0.072
,. f ( x) y 2 y y 3 y n,. x x2 x3 xn 0.050 0.049
x x 2 0.050 0.049
2 CART SupportVectorMachine 0.003 0.234 (0.22) 0.220 0.023 0.053 0.050 0.02 0.266 (0.259) 0.262 0.066 0.072 0.049
g() x { f xθ ; θ Θ} ( )