机器学习入门：线性回归及梯度下降（二）

本文是用C++对上一篇文章机器学习入门：线性回归及梯度下降（二）的实现

测试数据

特征变量维度dim=384
训练样本simple_size=25000 下载地址save_train
测试样本test_size=25000 下载地址save_test

测试代码

#include <iostream>#include <fstream>#include <string>#include <vector>#include <stdlib.h>#include <string.h>#include <math.h>using namespace std;#define varibleNum 384#define dimOfSpace varibleNum + 1#define learnTimes 2000// n = 384 R = {n+1} m = 25000static double numda = 0.1;class LiRegress{  private:    double thita[dimOfSpace];    double *residul;    vector<vector<double> > x;    vector<double> y;    vector<double> yresult;    ifstream file;    double alpha;    int m;    double costBefor, costAft;    // 解析某一行训练数据    void getOneTrainCase(string line)    {        string temp;        int left = -1; // 上次停留指针        vector<double> onecase;        for (int i = 0; i < line.length(); i++)        {            if (line[i] == ',') // 遇到,判断            {            if (left == -1)            {                //cout << "the " << atoi(line.substr(0, i).c_str()) << " th test case:" << endl;                onecase.push_back(1);            }            else            {                temp = line.substr(left, i - left);                onecase.push_back(atof(temp.c_str()));            }            left = i + 1;            }        }        x.push_back(onecase);        temp = line.substr(left, line.length() - 1); // 最后一个数是y值        y.push_back(atof(temp.c_str()));    }    // 解析某一行测试数据并预测    void getOneTestCase(string line)    {        string temp;        int left = -1;        vector<double> onecase;        for (int i = 0; i < line.length(); i++)        {            if (line[i] == ',')            {            if (left == -1)            {                //cout << "the " << atoi(line.substr(0, i).c_str()) << " th test case:" << endl;                onecase.push_back(1);            }            else            {                temp = line.substr(left, i - left);                onecase.push_back(atof(temp.c_str()));            }            left = i + 1;            }        }        temp = line.substr(left, line.length() - 1);        onecase.push_back(atof(temp.c_str()));        // y = thita*x 求出预测值        double ans = 0;        for (int i = 0; i < dimOfSpace; i++)        {            ans += onecase[i] * thita[i];        }        onecase.clear();        yresult.push_back(ans);    }    // 保存运算过程每次循环时Hthita数组，节省运算时间    void getResidulOfAllCases(double *_thita)    {        double ans;        for (int i = 0; i < m; i++)        {            ans = 0;            for (int j = 0; j < dimOfSpace; j++)            {            ans += x[i][j] * _thita[j];            }            residul[i] = ans;        }    }    // loss函数 使用经典的均方误差(MSE)计算    double CostFunction()    {        double jthita = 0;        for (int i = 0; i < m; i++)        {            jthita += pow(residul[i] - y[i], 2);        }        jthita *= 0.5 * 1 / (double)m;        return jthita;    }  public:    LiRegress()    {        // 初始化        memset(thita, 0, sizeof(thita));        residul = NULL;        alpha = 0.09;        m = 0;    };    LiRegress(char *filename)    {        memset(thita, 0, sizeof(thita));        residul = NULL;  // Hthita        alpha = 1.0;  // 下降梯度        m = 0; // simple_size        openFile(filename);    };    ~LiRegress()    {        free(thita);        free(residul);        x.clear();        y.clear();        yresult.clear();    };    double *get()    {        return thita;    }    void openFile(const char *filename)    {        file.open(filename);        if (!file.is_open())        {             cout << "error" << endl;            return;        }        string line;        getline(file, line); // 去除标题行        while (file.good())        {            getline(file, line);            if (!line.empty())            {                m++;                getOneTrainCase(line); // 逐行解析数据            }    }    cout << "over" << endl;        // 初始化        if (!residul)        {            free(residul);            residul = NULL;        }        residul = new double[m];        file.close();    }    void Repeat()    {        // Ԥ?????xi)        getResidulOfAllCases(thita);        costBefor = CostFunction();        bool equal = false;        int n = learnTimes;        while (n--)        {            costAft = gradientDecent(costBefor);            cout << learnTimes - n << " " << alpha << " " << costBefor << " " << costAft << " " << costAft - costBefor <<  endl;            // 调节alpha值以改进速率            if (learnTimes - n == 100)                alpha = 0.0984771;            if (costAft > costBefor) // 如果更新后loss变大，则减小alpha的值            {                alpha = 0.0984771;            }            // cost相等            else if (costAft == costBefor)            {                if (equal) // 连续相等，则认为找到了局部最小值                {                    break;                }                if (!equal) // 局部最小值之间左右震荡                {                    alpha *= 0.1;                    equal = true;                }            }            else            {                equal = false;                double radient = (costBefor - costAft) / costBefor;                if ((costBefor - costAft) < 0.0001)                {                    //alpha += 0.0005;                    costBefor = costAft;                    // cout << "over " << radient << " " << costBefor - costAft <<  endl;                    //break;                }                else                    costBefor = costAft; // 应用此更新            }        }    }    // 梯度下降    double gradientDecent(double costBefor)    {        // 根据当前thita数组计算Hthita数组        getResidulOfAllCases(thita);        double *temp = new double[dimOfSpace];        int i, j;        double sum;        for (j = 0; j < dimOfSpace; j++)        {            sum = 0;            for (i = 0; i < m; i++) // 梯度下降过程，num用来防止过拟合            {                sum += (residul[i] - y[i]) * x[i][j];            }            if (j == 0)                temp[j] = thita[j] - alpha * 1 / (double)m * sum;            else                temp[j] = thita[j] - alpha * 1 / (double)m * (sum - numda * thita[j]);        }        getResidulOfAllCases(temp);        double costAfter = CostFunction(); // 计算loss值        if (costAfter < costBefor) // 如果loss值减少，则沿下降方向移动        {            for (j = 0; j < dimOfSpace; j++)            {            thita[j] = temp[j];            }        }            delete[] temp;            return costAfter;        }    void readTest(const char *filename)    {        file.open(filename);        if (!file.is_open())        {             cout << "error" << endl;            return;        }        string line;        int num = 0;        getline(file, line);        while (file.good())        {            getline(file, line);            if (!line.empty())            {            num++;            getOneTestCase(line);            }        }        cout << "caculate over" << endl;        // 将结果写入文件爱呢        ofstream outfile("result.csv");        outfile << "Id,reference" << endl;        for (int i = 0; i < m; i++)        {            outfile << i << "," << yresult[i] << endl;        }        outfile.close();    }};int main(){    LiRegress *lg = new LiRegress();    lg->openFile("save_train.csv");    lg->Repeat();    lg->readTest("save_test.csv");    return 0;}

测试结果

刚开始alpha=0.9 下降速率很快

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500次迭代后下降速率就很慢了