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

#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
",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
",j,p1,p2,p3,ltheta);
                }
        }
        return 0;
}