使用C#實(shí)現(xiàn)簡(jiǎn)單的線(xiàn)性回歸的代碼詳解

更新時(shí)間：2024年01月12日 09:49:05 作者：Dm_dotnet

最近注意到了NumSharp,想學(xué)習(xí)一下,最好的學(xué)習(xí)方式就是去實(shí)踐,因此從github上找了一個(gè)用python實(shí)現(xiàn)的簡(jiǎn)單線(xiàn)性回歸代碼,然后基于NumSharp用C#進(jìn)行了改寫(xiě),需要的朋友可以參考下

前言

最近注意到了NumSharp，想學(xué)習(xí)一下，最好的學(xué)習(xí)方式就是去實(shí)踐，因此從github上找了一個(gè)用python實(shí)現(xiàn)的簡(jiǎn)單線(xiàn)性回歸代碼，然后基于NumSharp用C#進(jìn)行了改寫(xiě)。

NumSharp簡(jiǎn)介

NumSharp（NumPy for C#）是一個(gè)在C#中實(shí)現(xiàn)的多維數(shù)組操作庫(kù)，它的設(shè)計(jì)受到了Python中的NumPy庫(kù)的啟發(fā)。NumSharp提供了類(lèi)似于NumPy的數(shù)組對(duì)象，以及對(duì)這些數(shù)組進(jìn)行操作的豐富功能。它是一個(gè)開(kāi)源項(xiàng)目，旨在為C#開(kāi)發(fā)者提供在科學(xué)計(jì)算、數(shù)據(jù)分析和機(jī)器學(xué)習(xí)等領(lǐng)域進(jìn)行高效數(shù)組處理的工具。

python代碼

用到的python代碼來(lái)源：https://github.com/llSourcell/linear_regression_live

下載到本地之后，如下圖所示：

python代碼如下所示：

#The optimal values of m and b can be actually calculated with way less effort than doing a linear regression. 
#this is just to demonstrate gradient descent
?
from numpy import *
?
# y = mx + b
# m is slope, b is y-intercept
def compute_error_for_line_given_points(b, m, points):
    totalError = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        totalError += (y - (m * x + b)) ** 2
    return totalError / float(len(points))
?
def step_gradient(b_current, m_current, points, learningRate):
    b_gradient = 0
    m_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
    new_b = b_current - (learningRate * b_gradient)
    new_m = m_current - (learningRate * m_gradient)
    return [new_b, new_m]
?
def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
    b = starting_b
    m = starting_m
    for i in range(num_iterations):
        b, m = step_gradient(b, m, array(points), learning_rate)
    return [b, m]
?
def run():
    points = genfromtxt("data.csv", delimiter=",")
    learning_rate = 0.0001
    initial_b = 0 # initial y-intercept guess
    initial_m = 0 # initial slope guess
    num_iterations = 1000
    print ("Starting gradient descent at b = {0}, m = {1}, error = {2}".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points)))
    print ("Running...")
    [b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
    print ("After {0} iterations b = {1}, m = {2}, error = {3}".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points)))
?
if __name__ == '__main__':
    run()

用C#進(jìn)行改寫(xiě)

首先創(chuàng)建一個(gè)C#控制臺(tái)應(yīng)用，添加NumSharp包：

現(xiàn)在我們開(kāi)始一步步用C#進(jìn)行改寫(xiě)。

python代碼：

points = genfromtxt("data.csv", delimiter=",")

在NumSharp中沒(méi)有g(shù)enfromtxt方法需要自己寫(xiě)一個(gè)。

C#代碼：

 //創(chuàng)建double類(lèi)型的列表
 List<double> Array = new List<double>();
?
 // 指定CSV文件的路徑
 string filePath = "你的data.csv路徑";
?
 // 調(diào)用ReadCsv方法讀取CSV文件數(shù)據(jù)
 Array = ReadCsv(filePath);
?
 var array = np.array(Array).reshape(100,2);
?
static List<double> ReadCsv(string filePath)
{
    List<double> array = new List<double>();
    try
    {
        // 使用File.ReadAllLines讀取CSV文件的所有行
        string[] lines = File.ReadAllLines(filePath);             
?
        // 遍歷每一行數(shù)據(jù)
        foreach (string line in lines)
        {
            // 使用逗號(hào)分隔符拆分每一行的數(shù)據(jù)
            string[] values = line.Split(',');
?
            // 打印每一行的數(shù)據(jù)
            foreach (string value in values)
            {
                array.Add(Convert.ToDouble(value));
            }                  
        }
    }
    catch (Exception ex)
    {
        Console.WriteLine("發(fā)生錯(cuò)誤: " + ex.Message);
    }
    return array;
}

python代碼：

def compute_error_for_line_given_points(b, m, points):
    totalError = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        totalError += (y - (m * x + b)) ** 2
    return totalError / float(len(points))

這是在計(jì)算均方誤差:

C#代碼：

 public static double compute_error_for_line_given_points(double b,double m,NDArray array)
 {
     double totalError = 0;
     for(int i = 0;i < array.shape[0];i++)
     {
         double x = array[i, 0];
         double y = array[i, 1];
         totalError += Math.Pow((y - (m*x+b)),2);
     }
     return totalError / array.shape[0];
 }

python代碼：

def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
    b = starting_b
    m = starting_m
    for i in range(num_iterations):
        b, m = step_gradient(b, m, array(points), learning_rate)
    return [b, m]

def step_gradient(b_current, m_current, points, learningRate):
    b_gradient = 0
    m_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
    new_b = b_current - (learningRate * b_gradient)
    new_m = m_current - (learningRate * m_gradient)
    return [new_b, new_m]

這是在用梯度下降來(lái)迭代更新y = mx + b中參數(shù)b、m的值。

因?yàn)樵诒纠?，誤差的大小是通過(guò)均方差來(lái)體現(xiàn)的，所以均方差就是成本函數(shù)（cost function）或者叫損失函數(shù)（loss function），我們想要找到一組b、m的值，讓誤差最小。

成本函數(shù)如下：

對(duì)θ1求偏導(dǎo)，θ1就相當(dāng)于y = mx + b中的b：

再對(duì)θ2求偏導(dǎo)，θ2就相當(dāng)于y = mx + b中的m：

使用梯度下降：

θ1與θ2的表示：

α是學(xué)習(xí)率，首先θ1、θ2先隨機(jī)設(shè)一個(gè)值，剛開(kāi)始梯度變化很大，后面慢慢趨于0，當(dāng)梯度等于0時(shí)，θ1與θ2的值就不會(huì)改變了，或者達(dá)到我們?cè)O(shè)置的迭代次數(shù)了，就不再繼續(xù)迭代了。關(guān)于原理這方面的解釋?zhuān)梢圆榭催@個(gè)鏈接（https://www.geeksforgeeks.org/ml-linear-regression/），本文中使用的圖片也來(lái)自這里。

總之上面的python代碼在用梯度下降迭代來(lái)找最合適的參數(shù)，現(xiàn)在用C#進(jìn)行改寫(xiě)：

 public static double[] gradient_descent_runner(NDArray array, double starting_b, double starting_m, double learningRate,double num_iterations)
 {
     double[] args = new double[2];
     args[0] = starting_b;
     args[1] = starting_m;
?
     for(int i = 0 ; i < num_iterations; i++) 
     {
         args = step_gradient(args[0], args[1], array, learningRate);
     }
?
     return args;
 }

 public static double[] step_gradient(double b_current,double m_current,NDArray array,double learningRate)
 {
     double[] args = new double[2];
     double b_gradient = 0;
     double m_gradient = 0;
     double N = array.shape[0];
?
     for (int i = 0; i < array.shape[0]; i++)
     {
         double x = array[i, 0];
         double y = array[i, 1];
         b_gradient += -(2 / N) * (y - ((m_current * x) + b_current));
         m_gradient += -(2 / N) * x * (y - ((m_current * x) + b_current));
     }
?
     double new_b = b_current - (learningRate * b_gradient);
     double new_m = m_current - (learningRate * m_gradient);
     args[0] = new_b;
     args[1] = new_m;
?
     return args;
 }

用C#改寫(xiě)的全部代碼：

using NumSharp;
?
namespace LinearRegressionDemo
{
    internal class Program
    {    
        static void Main(string[] args)
        {   
            //創(chuàng)建double類(lèi)型的列表
            List<double> Array = new List<double>();
?
            // 指定CSV文件的路徑
            string filePath = "你的data.csv路徑";
?
            // 調(diào)用ReadCsv方法讀取CSV文件數(shù)據(jù)
            Array = ReadCsv(filePath);
?
            var array = np.array(Array).reshape(100,2);
?
            double learning_rate = 0.0001;
            double initial_b = 0;
            double initial_m = 0;
            double num_iterations = 1000;
?
            Console.WriteLine($"Starting gradient descent at b = {initial_b}, m = {initial_m}, error = {compute_error_for_line_given_points(initial_b, initial_m, array)}");
            Console.WriteLine("Running...");
            double[] Args =gradient_descent_runner(array, initial_b, initial_m, learning_rate, num_iterations);
            Console.WriteLine($"After {num_iterations} iterations b = {Args[0]}, m = {Args[1]}, error = {compute_error_for_line_given_points(Args[0], Args[1], array)}");
            Console.ReadLine();
?
        }
?
        static List<double> ReadCsv(string filePath)
        {
            List<double> array = new List<double>();
            try
            {
                // 使用File.ReadAllLines讀取CSV文件的所有行
                string[] lines = File.ReadAllLines(filePath);             
?
                // 遍歷每一行數(shù)據(jù)
                foreach (string line in lines)
                {
                    // 使用逗號(hào)分隔符拆分每一行的數(shù)據(jù)
                    string[] values = line.Split(',');
?
                    // 打印每一行的數(shù)據(jù)
                    foreach (string value in values)
                    {
                        array.Add(Convert.ToDouble(value));
                    }                  
                }
            }
            catch (Exception ex)
            {
                Console.WriteLine("發(fā)生錯(cuò)誤: " + ex.Message);
            }
            return array;
        }
?
        public static double compute_error_for_line_given_points(double b,double m,NDArray array)
        {
            double totalError = 0;
            for(int i = 0;i < array.shape[0];i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                totalError += Math.Pow((y - (m*x+b)),2);
            }
            return totalError / array.shape[0];
        }
?
        public static double[] step_gradient(double b_current,double m_current,NDArray array,double learningRate)
        {
            double[] args = new double[2];
            double b_gradient = 0;
            double m_gradient = 0;
            double N = array.shape[0];
?
            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                b_gradient += -(2 / N) * (y - ((m_current * x) + b_current));
                m_gradient += -(2 / N) * x * (y - ((m_current * x) + b_current));
            }
?
            double new_b = b_current - (learningRate * b_gradient);
            double new_m = m_current - (learningRate * m_gradient);
            args[0] = new_b;
            args[1] = new_m;
?
            return args;
        }
?
        public static double[] gradient_descent_runner(NDArray array, double starting_b, double starting_m, double learningRate,double num_iterations)
        {
            double[] args = new double[2];
            args[0] = starting_b;
            args[1] = starting_m;
?
            for(int i = 0 ; i < num_iterations; i++) 
            {
                args = step_gradient(args[0], args[1], array, learningRate);
            }
?
            return args;
        }
?
?
    }
}

python代碼的運(yùn)行結(jié)果：