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

1. #include "stdio.h"
2. #include "math.h"
3. double matrix[9][4]={{1,47,76,24}, //include x0=1
4. {1,46,77,23},
5. {1,48,74,22},
6. {1,34,76,21},
7. {1,35,75,24},
8. {1,34,77,25},
9. {1,55,76,21},
10. {1,56,74,22},
11. {1,55,72,22},
12. };
13. double result[]={1,
14. 1,
15. 1,
16. 2,
17. 2,
18. 2,
19. 3,
20. 3,
21. 3,};
22. double theta[2][4]={
23. {0.3,0.3,0.01,0.01},
24. {0.5,0.5,0.01,0.01}}; // include theta0
25. double function_g(double x)
26. {
27. double ex = pow(2.718281828,x);
28. return ex/(1+ex);
29. }
30. double function_e(double x)
31. {
32. return pow(2.718281828,x);
33. }
34. int main(void)
35. {
36. double likelyhood = 0.0;
37. for(int j = 0;j<9;++j)
38. {
39. double sum = 1.0; // this is very important, because exp(thetak x)=1
40. for(int l = 0;l<2;++l)
41. {
42. double xi = 0.0;
43. for(int k=0;k<4;++k)
44. {
45. xi += matrix[j][k]*theta[l][k];
46. }
47. sum += function_e(xi);
48. }
49. double xi = 0.0;
50. for(int k=0;k<4;++k)
51. {
52. xi += matrix[j][k]*theta[0][k];
53. }
54. double p1 = function_e(xi)/sum;
55. xi = 0.0;
56. for(int k=0;k<4;++k)
57. {
58. xi += matrix[j][k]*theta[1][k];
59. }
60. double p2 = function_e(xi)/sum;
61. double p3 = 1-p1-p2;
62. double ltheta = 0.0;
63. if(result[j]==1)
64. ltheta = log(p1);
65. else if(result[j]==2)
66. ltheta = log(p2);
67. else if(result[j]==3)
68. ltheta = log(p3);
69. else
70. {}
71. printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);
72. }
73. for(int i =0 ;i<1000;++i)
74. {
75. for(int j=0;j<9;++j)
76. {
77. double sum = 1.0; // this is very important, because exp(thetak x)=1
78. for(int l = 0;l<2;++l)
79. {
80. double xi = 0.0;
81. for(int k=0;k<4;++k)
82. {
83. xi += matrix[j][k]*theta[l][k];
84. }
85. sum += function_e(xi);
86. }
87. double xi = 0.0;
88. for(int k=0;k<4;++k)
89. {
90. xi += matrix[j][k]*theta[0][k];
91. }
92. double p1 = function_e(xi)/sum;
93. xi = 0.0;
94. for(int k=0;k<4;++k)
95. {
96. xi += matrix[j][k]*theta[1][k];
97. }
98. double p2 = function_e(xi)/sum;
99. double p3 = 1-p1-p2;
100. for(int m = 0; m<4; ++m)
101. {
102. if(result[j]==1)
103. {
104. theta[0][m] = theta[0][m] + 0.001*(1-p1)*matrix[j][m];
105. }
106. else
107. {
108. theta[0][m] = theta[0][m] + 0.001*(-p1)*matrix[j][m];
109. }
110. if(result[j]==2)
111. {
112. theta[1][m] = theta[1][m] + 0.001*(1-p2)*matrix[j][m];
113. }
114. else
115. {
116. theta[1][m] = theta[1][m] + 0.001*(-p2)*matrix[j][m];
117. }
118. }
119. }
120. double likelyhood = 0.0;
121. for(int j = 0;j<9;++j)
122. {
123. double sum = 1.0; // this is very important, because exp(thetak x)=1
124. for(int l = 0;l<2;++l)
125. {
126. double xi = 0.0;
127. for(int k=0;k<4;++k)
128. {
129. xi += matrix[j][k]*theta[l][k];
130. }
131. sum += function_e(xi);
132. }
133. double xi = 0.0;
134. for(int k=0;k<4;++k)
135. {
136. xi += matrix[j][k]*theta[0][k];
137. }
138. double p1 = function_e(xi)/sum;
139. xi = 0.0;
140. for(int k=0;k<4;++k)
141. {
142. xi += matrix[j][k]*theta[1][k];
143. }
144. double p2 = function_e(xi)/sum;
145. double p3 = 1-p1-p2;
146. double ltheta = 0.0;
147. if(result[j]==1)
148. ltheta = log(p1);
149. else if(result[j]==2)
150. ltheta = log(p2);
151. else if(result[j]==3)
152. ltheta = log(p3);
153. else
154. {}
155. printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);
156. }
157. }
158. return 0;
159. }