《机器学习》case-based

山T X1<+9,X2<9andX2<X1

1 , 2 and X2 1 - X ⎯⎯ X ⎯⎯ ⎯⎯ X + −

X See-Saw ap Float Figure 1: A flush tank nthesis Samey Synthesized Desig as the depth of water(D)in the tank increases, the rate of flow of water into the tank(Q)should decrease O<D

as the depth of water(D) in the tank increases,the rate of flow of water into the tank(Q) should decrease. Q⎯⎯ D −

1. The function of function( chainrule etuFf(x, y), z=gu, v) z z [-]=[-].[] O L 2. The total influence rule Let uf(x,y) au [△a]=[-」×[△x]+ ]×[Ay] OX 1. Inverse application of the function of function rule Opl Op2 z -x op3 x 3×O Dp2=Op

1. The function of function(chain)rule Let u=f(x,y), z=g(u,v) [ ] [ ].[ ] x u u z x z     =   2. The total influence rule Let u=f(x,y) [ ] [ ] [ ] [ ] [ y] y u x x u u       +    = 1. Inverse application of the function of function rule: 3 2 1 z 1 1 Op3 2 Op Op Op z x Var x Op Op  = ⎯⎯ ⎯⎯ ⎯⎯

2. Inverse application of the total differential rule R<。b-小 Op4 Varl、Op2 Op5 Op3 Var2 Qp4xOp2+05×p3=Op

2. Inverse application of the total differential rule u v ⎯Op1 ⎯ Var1 Var2 u v Op4 Op2 Op5 Op3 Op4Op2 + Op5Op3 = Op1

Q<Var2<varl<T-D Q<Var2<-VarlT-D O<Var2<-varl-D

Q Var Var D Q Var Var D Q Var Var D ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ ⎯⎯ + + − + − + − + + 2 1 2 1 2 1