SoftMax regression

最终收敛到这个结果，巨爽。

smaple 0: 0.983690,0.004888,0.011422,likelyhood:-0.016445

smaple 1: 0.940236,0.047957,0.011807,likelyhood:-0.061625

smaple 2: 0.818187,0.001651,0.180162,likelyhood:-0.200665

smaple 3: 0.000187,0.999813,0.000000,likelyhood:-0.000187

smaple 4: 0.007913,0.992087,0.000000,likelyhood:-0.007945

smaple 5: 0.001585,0.998415,0.000000,likelyhood:-0.001587

smaple 6: 0.020159,0.000001,0.979840,likelyhood:-0.020366

smaple 7: 0.018230,0.000000,0.981770,likelyhood:-0.018398

smaple 8: 0.025072,0.000000,0.974928,likelyhood:-0.025392

[cpp]
view plaincopy

#include "stdio.h"
#include "math.h"

double matrix[9][4]={{1,47,76,24}, //include x0=1
{1,46,77,23},
{1,48,74,22},
{1,34,76,21},
{1,35,75,24},
{1,34,77,25},
{1,55,76,21},
{1,56,74,22},
{1,55,72,22},
};

double result[]={1,
1,
1,
2,
2,
2,
3,
3,
3,};

double theta[2][4]={
{0.3,0.3,0.01,0.01},
{0.5,0.5,0.01,0.01}}; // include theta0

double function_g(double x)
{
double ex = pow(2.718281828,x);
return ex/(1+ex);
}

double function_e(double x)
{
return pow(2.718281828,x);
}

int main(void)
{
double likelyhood = 0.0;
for(int j = 0;j<9;++j)
{
double sum = 1.0; // this is very important, because exp(thetak x)=1
for(int l = 0;l<2;++l)
{
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[l][k];

}
sum += function_e(xi);
}
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[0][k];

}
double p1 = function_e(xi)/sum;
xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[1][k];

}
double p2 = function_e(xi)/sum;
double p3 = 1-p1-p2;

double ltheta = 0.0;
if(result[j]==1)
ltheta = log(p1);
else if(result[j]==2)
ltheta = log(p2);
else if(result[j]==3)
ltheta = log(p3);
else
{}
printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);

}

for(int i =0 ;i<1000;++i)
{
for(int j=0;j<9;++j)
{
double sum = 1.0; // this is very important, because exp(thetak x)=1
for(int l = 0;l<2;++l)
{
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[l][k];

}
sum += function_e(xi);
}
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[0][k];

}
double p1 = function_e(xi)/sum;
xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[1][k];

}
double p2 = function_e(xi)/sum;
double p3 = 1-p1-p2;
for(int m = 0; m<4; ++m)
{
if(result[j]==1)
{
theta[0][m] = theta[0][m] + 0.001*(1-p1)*matrix[j][m];
}
else
{
theta[0][m] = theta[0][m] + 0.001*(-p1)*matrix[j][m];
}
if(result[j]==2)
{
theta[1][m] = theta[1][m] + 0.001*(1-p2)*matrix[j][m];
}
else
{
theta[1][m] = theta[1][m] + 0.001*(-p2)*matrix[j][m];
}
}
}
double likelyhood = 0.0;
for(int j = 0;j<9;++j)
{
double sum = 1.0; // this is very important, because exp(thetak x)=1
for(int l = 0;l<2;++l)
{
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[l][k];

}
sum += function_e(xi);
}
double xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[0][k];

}
double p1 = function_e(xi)/sum;
xi = 0.0;
for(int k=0;k<4;++k)
{
xi += matrix[j][k]*theta[1][k];

}
double p2 = function_e(xi)/sum;
double p3 = 1-p1-p2;

double ltheta = 0.0;
if(result[j]==1)
ltheta = log(p1);
else if(result[j]==2)
ltheta = log(p2);
else if(result[j]==3)
ltheta = log(p3);
else
{}
printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);
}
}
return 0;
}