勾配法と確率的最適化による学習例：

# ２変数からなる16種類のロジック
x=matrix(c(1,1,1,1,1,0,1,0,1,1,0,0),ncol=4);
y=matrix(c(0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,1,1,0,1,0,1,1,0,0,1,0,
1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,1,1,1,1),byrow=T,ncol=4)
> x # input matrix
[,1] [,2] [,3] [,4]
[1,] 1 1 1 1 # X0
[2,] 1 1 0 0 # X1
[3,] 1 0 1 0 # X2
> y
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0 # none
[2,] 0 0 0 1 # notX1 & notX2
[3,] 0 0 1 0 # notX1 & X2
[4,] 0 1 0 0 # X1 & notX2
[5,] 1 0 0 0 # X1 & X2
[6,] 0 0 1 1 # notX1
[7,] 0 1 0 1 # notX2
[8,] 1 0 0 1 # {X1 & X2} or {notX1 & notX2}
[9,] 0 1 1 0 # {X1 & notX2} or {notX1 & X2}
[10,] 1 0 1 0 # X2
[11,] 1 1 0 0 # X1
[12,] 1 1 1 0 # X1 or X2
[13,] 1 1 0 1 # X1 or notX2
[14,] 1 0 1 1 # notX1 or X2
[15,] 0 1 1 1 # notX1 or notX2
[16,] 1 1 1 1 # all
# 勾配法
stepSize=0.1;gamma=5;logicID=2;
w=matrix(rnorm(3),nrow=1);
for (i_tr in 1:2000) {
for (i_inst in 1:4){
a=w%*%x[,i_inst,drop=F]
s=1/(1+exp(-gamma*a))
w=w+stepSize*(y[logicID,i_inst]-s)*s*(1-s)*gamma*x[,i_inst]
}
}
for (i_inst in 1:4){
a=w%*%x[,i_inst,drop=F]
print(1/(1+exp(-gamma*a)))
}
# 確率的最適化法（焼きなまし法）
gamma=2;logicID=2;
w=matrix(rnorm(3),nrow=1);
err=4;width=1;sTemp=matrix(0,nrow=1,ncol=3);C=0.25
for (i_tr in 1:5000) {
wTemp=w+rnorm(3,mean=0,sd=width)
for (i_inst in 1:4) {
a=wTemp%*%x[,i_inst,drop=F]
sTemp[i_inst]=1/(1+exp(-gamma*a))
}
errTemp=sum((sTemp-y[logicID,])^2)
delta=errTemp-err;
prob=1/(1+exp(delta/(C*width)))
if (runif(1) < prob) {
w=wTemp
err=errTemp
}
width=width*0.99
}
for (i_inst in 1:4) {
a=w%*%x[,i_inst,drop=F]
print(1/(1+exp(-gamma*a)))
}

*Related*