简单的一元线性回归算法已经在这里“C语言简单的一元线性回归算法”，并且也简单阐述了梯度求解推导过程。
今天我们再呈上多元线性回归算法梯度下降的C语言实现，代码中已经加入了相应的注释。如下：
MultipleLinearRegression.h
#ifndef MULTIPLELINEARREGRESSION_MULTIPLELINEARREGRESSION_H#define MULTIPLELINEARREGRESSION_MULTIPLELINEARREGRESSION_H//设置样本数为 10#define SAMPLE_COUNT 10//设置参数个数为 6#define PARAMETER_COUNT 6void init(double learning_rate, long int X_Len,long int X_arg_count,int channel);void fit(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT],double temp[PARAMETER_COUNT],double theta[PARAMETER_COUNT]);double _f(const double train_x[PARAMETER_COUNT],double theta[PARAMETER_COUNT]);double* predict(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double theta[PARAMETER_COUNT]);double loss(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT], double temp[PARAMETER_COUNT],double *loss_val);void calc_gradient(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT],double *temp,double *theta);void train_step(double temp[PARAMETER_COUNT],double theta[PARAMETER_COUNT]);#endif //MULTIPLELINEARREGRESSION_MULTIPLELINEARREGRESSION_HMultipleLinearRegression.h
#include "MultipleLinearRegression.h"#include <stdio.h>#include <malloc.h>//int type_count = 5;int g_X_Len = 10;double g_learning_rate = 0.01;int g_X_arg_count = 5;int g_channel = 1;double g_out_Y_pt = 0;//预测输出值指针double *y_pred_pt = 0;//损失值double loss_val[1] = {1.0};/* * learning_rate 学习率 * * X_Len 样本个数 * * X_arg_count 参数个数 * * channel 通道数<暂未考虑> * */void init(double learning_rate, long int X_Len,long int X_arg_count,int channel){ g_learning_rate = learning_rate; g_X_Len = X_Len; g_X_arg_count = X_arg_count; g_channel = channel; y_pred_pt = malloc((size_t) X_Len);}void fit(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT], double temp[PARAMETER_COUNT],double theta[PARAMETER_COUNT]){ for (int i = 0; i < 10000; ++i) { printf("step %d: n", i); calc_gradient(train_x,train_y,temp,theta); loss_val[0] = loss(train_x,train_y,theta,loss_val); }}double _f(const double train_x[PARAMETER_COUNT],double theta[PARAMETER_COUNT]){ g_out_Y_pt = -1; for (int i = 0; i < PARAMETER_COUNT; ++i) { g_out_Y_pt += theta[i]*train_x[i]; } return g_out_Y_pt;}//预测double* predict(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double theta[PARAMETER_COUNT]){ for (int i = 0; i < SAMPLE_COUNT; ++i) { y_pred_pt[i] = _f(train_x[i],theta); } return y_pred_pt;}//求损失double loss(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT], double theta[PARAMETER_COUNT],double *loss_val){ predict(train_x,theta); loss_val[0] = -1; for (int i = 0; i < SAMPLE_COUNT; i++) { loss_val[0] += (train_y[i] - y_pred_pt[i]) * (train_y[i] - y_pred_pt[i]); } loss_val[0] = loss_val[0] / SAMPLE_COUNT; printf(" loss_val = %fn", loss_val[0]); return loss_val[0];}//求梯度void calc_gradient(double train_x[SAMPLE_COUNT][PARAMETER_COUNT],double train_y[PARAMETER_COUNT], double temp[PARAMETER_COUNT], double theta[PARAMETER_COUNT]) { for (int i = 0; i < g_X_arg_count -1; i++) { double sum = 0; for (int j = 0; j < g_X_Len; j++) { double hx = 0; for (int k = 0; k < g_X_arg_count; k++) { hx += theta[k] * train_x[j][k]; } sum += (hx - train_y[j]) * train_x[j][i]; } temp[i] = sum / g_X_Len * 0.01; } printf("n--------------------n"); train_step(temp, theta);}//更新参数值void train_step(double temp[PARAMETER_COUNT],double theta[PARAMETER_COUNT]) { for (int i = 0; i < g_X_arg_count - 1; i++) { theta[i] = theta[i] - temp[i]; printf(" theta[%d] = %fn",i, theta[i]); }}main.c
//#include "src/LinerRegression.h"#include "utils/util.h"#include "src/MultipleLinearRegression.h"int main() { // 初始数据 设置为 5个维度；增加第一维为 1 即为 常量值 b //该数据由 Y= 4*X1 + 9*X2 + 10*X3 + 2*X4 + 1*X5 + 6 产生(数据中尚为加入噪声) double X_pt[10][6] = {{1, 7.41, 3.98, 8.34, 8.0, 0.95}, {1, 6.26, 5.12, 9.57, 0.3, 7.79}, {1, 1.52, 1.95, 4.01, 7.96, 2.19}, {1, 1.91, 8.58, 6.64, 2.99, 2.18}, {1, 2.2, 6.88, 0.88, 0.5, 9.74}, {1, 5.17, 0.14, 4.09, 9.0, 2.63}, {1, 9.13, 5.54, 6.36, 9.98, 5.27}, {1, 1.17, 4.67, 9.02, 5.14, 3.46}, {1, 3.97, 6.72, 6.12, 9.42, 1.43}, {1, 0.27, 3.16, 7.07, 0.28, 1.77}}; double Y_pt[10] = {171.81, 181.21, 87.84, 165.42, 96.26, 89.47, 181.21, 156.65, 163.83, 108.55}; //初始参数函数 temp 只是一个临时变量 double temp[6] = {1.0,1.0,1.0,1.0,1.0,1.0}; double theta[6] = {1.0,1.0,1.0,1.0,1.0,1.0}; //初始化相关参数 init(0.01,10,5+1,1); fit(X_pt,Y_pt,temp,theta); return 0;}可以看到再训练10000次的时候损失已经比较小了，各个参数也已经接应我们预设的参数了
step 9999:-------------------- theta[0] = 5.994281 theta[1] = 3.999957 theta[2] = 9.000404 theta[3] = 10.000375 theta[4] = 2.000242 loss_val = 0.900745Process finished with exit code 0
这只是一个C语言的简单实现，学习率也设定的是固定值，训练次数也设定为固定值。如果各位大侠有其他比较好的实现方式欢迎留言推荐。另外由于很久很久不用C语言开发了，肯定会有语法的不完美。如有更好的建议或者其他疑问欢迎交流，小弟恭候。