c/c++實現簡單線性迴歸問題(機器學習入門實例)

線性迴歸問題簡單分析

個人簡單分析，有問題歡迎評論討論

如果給出很多組數據（x,y），求擬合一條y=wx+b直線模擬問題，高中數學也有提到過，就是求w,b兩個參數，使得擬合的直線可以近似穿過目標數據區域的中間位置，儘可以使得更多的真實數據點落在擬合的直線上。這個問題常常出現在機器學習，深度學習的入門教程的前幾個例子中，然而無奈網上教程都是用機器學習常用的python進行實現，作爲一個習慣c/c++的強類型語言的個人來說，看到python沒有類型標識簡直看出強迫症和雲裏霧裏的感覺（寫完感慨python真香，然而現在還不咋習慣）。

因此我打算自己動手用c++來寫一遍，希望能加深一下理解。對於給出的數據點集，通過迭代循環的手段進行優化w和b兩個參數，迭代一次w，b的值更準確一次，而迭代n次運用的方法就是老生常談的梯度下降法，經過n次迭代後得到的w和b就很準確了。而每一次迭代需要進行求導計算w(b)=w(b)-learningrate*▲w’(b’),具體過程可以求▲w’(b’)的平均值效果更好，learningrate學習率是用來控制下降的高度的，每次降太快容易越過極小值點。

那麼，如何去衡量b直線的w和b準不準確呢，衡量的方法是累計（yi-yi’)^2的值， 定義成一個loss損失函數進行評估。

運行結果：具體結果和第一個圖還是很接近的，數據點集和代碼在下方

c++重寫實現

#include<bits/stdc++.h>

using namespace std;
typedef long double ld;
vector<ld> XArray;
vector<ld> YArray;
ld end_b,end_w;
ld learning_rate = 0.0001;
ld initial_b = 0;
ld initial_w = 0;
int num_iterations=5000;

//處理csv文件得到數據點集
void getData(){
    ifstream inFile("data.csv", ios::in);
    string lineStr;
    vector<vector<string>> strArray;
    while(getline(inFile,lineStr)){
        stringstream ss(lineStr);
        string str;
        while(getline(ss,str,',')){
            XArray.push_back(stod(str));
            getline(ss,str,',');
            YArray.push_back(stod(str));
        }
     }
    // for(int i=0;i<XArray.size();i++){
    //     cout<<XArray[i]<<" "<<YArray[i]<<endl;
    // }
}
//衡量精確度的方法：loss函數
ld compute_error_for_line_given_points(ld b,ld w){
    ld totalError = 0;
    for(int i=0;i<XArray.size();i++){
        ld x =XArray[i];
        ld y =YArray[i];
        totalError += (y - (w * x + b))*(y - (w * x + b));
    }
    return totalError / ld(XArray.size());
}
//每次下降的具體做法：求導變化
vector<ld> step_gradient(ld b_current,ld w_current,ld learningRate){
    ld b_gradient = 0;
    ld w_gradient = 0;
    vector<ld> temp;
    int NumOfData = XArray.size();
    for(int i=0;i<NumOfData;i++){
        ld x = XArray[i];
        ld y = YArray[i];
        b_gradient += -(2.0/NumOfData) * (y - ((w_current * x) + b_current));
        w_gradient += -(2.0/NumOfData) * x * (y - ((w_current * x) + b_current));
    }
    temp.push_back(b_current - (learningRate * b_gradient));
    temp.push_back(w_current - (learningRate * w_gradient));
    return temp;
}
    
//梯度下降法，迭代次數num_iterations
void gradient_descent_runner(ld b,ld w,int lr,int num_iterations){
    ld t_b = b;
    ld t_w = w;
    for(int i=0;i<num_iterations;i++){
        vector<ld> v = step_gradient(t_b, t_w,learning_rate);
        t_b = v[0];
        t_w = v[1];
    }
    end_b=t_b;
    end_w=t_w;
}
int main(){
    getData();
    cout<<"Starting gradient descent at b = "<<initial_b
        <<" , w = "<<initial_w<<" , error = "
        <<compute_error_for_line_given_points(initial_b, initial_w)<<endl;
    cout<<"Running..."<<endl;
    gradient_descent_runner(initial_b, initial_w, learning_rate, num_iterations);
    cout<<"After "<<num_iterations<<" iterations b = "<<end_b
        <<" , w = "<<end_w<<" , error = "
        <<compute_error_for_line_given_points(end_b, end_w)<<endl;
    return 0;
}

原本的python實現

import numpy as np

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

def step_gradient(b_current, w_current, points, learningRate):
    b_gradient = 0
    w_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 - ((w_current * x) + b_current))
        w_gradient += -(2/N) * x * (y - ((w_current * x) + b_current))
    new_b = b_current - (learningRate * b_gradient)
    new_w = w_current - (learningRate * w_gradient)
    return [new_b, new_w]

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, np.array(points), learning_rate)
    return [b, m]

def run():
    points = np.genfromtxt("data.csv", delimiter=",")
    learning_rate = 0.0001
    initial_b = 0 # initial y-intercept guess
    initial_w = 0 # initial slope guess
    num_iterations = 5000
    print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
          .format(initial_b, initial_w,
                  compute_error_for_line_given_points(initial_b, initial_w, points))
          )
    print("Running...")
    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
    print("After {0} iterations b = {1}, w = {2}, error = {3}".
          format(num_iterations, b, w,
                 compute_error_for_line_given_points(b, w, points))
          )

if __name__ == '__main__':
    run()

data.csv數據文件

32.502345269453031,31.70700584656992
53.426804033275019,68.77759598163891
61.530358025636438,62.562382297945803
47.475639634786098,71.546632233567777
59.813207869512318,87.230925133687393
55.142188413943821,78.211518270799232
52.211796692214001,79.64197304980874
39.299566694317065,59.171489321869508
48.10504169176825,75.331242297063056
52.550014442733818,71.300879886850353
45.419730144973755,55.165677145959123
54.351634881228918,82.478846757497919
44.164049496773352,62.008923245725825
58.16847071685779,75.392870425994957
56.727208057096611,81.43619215887864
48.955888566093719,60.723602440673965
44.687196231480904,82.892503731453715
60.297326851333466,97.379896862166078
45.618643772955828,48.847153317355072
38.816817537445637,56.877213186268506
66.189816606752601,83.878564664602763
65.41605174513407,118.59121730252249
47.48120860786787,57.251819462268969
41.57564261748702,51.391744079832307
51.84518690563943,75.380651665312357
59.370822011089523,74.765564032151374
57.31000343834809,95.455052922574737
63.615561251453308,95.229366017555307
46.737619407976972,79.052406169565586
50.556760148547767,83.432071421323712
52.223996085553047,63.358790317497878
35.567830047746632,41.412885303700563
42.436476944055642,76.617341280074044
58.16454011019286,96.769566426108199
57.504447615341789,74.084130116602523
45.440530725319981,66.588144414228594
61.89622268029126,77.768482417793024
33.093831736163963,50.719588912312084
36.436009511386871,62.124570818071781
37.675654860850742,60.810246649902211
44.555608383275356,52.682983366387781
43.318282631865721,58.569824717692867
50.073145632289034,82.905981485070512
43.870612645218372,61.424709804339123
62.997480747553091,115.24415280079529
32.669043763467187,45.570588823376085
40.166899008703702,54.084054796223612
53.575077531673656,87.994452758110413
33.864214971778239,52.725494375900425
64.707138666121296,93.576118692658241
38.119824026822805,80.166275447370964
44.502538064645101,65.101711570560326
40.599538384552318,65.562301260400375
41.720676356341293,65.280886920822823
51.088634678336796,73.434641546324301
55.078095904923202,71.13972785861894
41.377726534895203,79.102829683549857
62.494697427269791,86.520538440347153
49.203887540826003,84.742697807826218
41.102685187349664,59.358850248624933
41.182016105169822,61.684037524833627
50.186389494880601,69.847604158249183
52.378446219236217,86.098291205774103
50.135485486286122,59.108839267699643
33.644706006191782,69.89968164362763
39.557901222906828,44.862490711164398
56.130388816875467,85.498067778840223
57.362052133238237,95.536686846467219
60.269214393997906,70.251934419771587
35.678093889410732,52.721734964774988
31.588116998132829,50.392670135079896
53.66093226167304,63.642398775657753
46.682228649471917,72.247251068662365
43.107820219102464,57.812512976181402
70.34607561504933,104.25710158543822
44.492855880854073,86.642020318822006
57.50453330326841,91.486778000110135
36.930076609191808,55.231660886212836
55.805733357942742,79.550436678507609
38.954769073377065,44.847124242467601
56.901214702247074,80.207523139682763
56.868900661384046,83.14274979204346
34.33312470421609,55.723489260543914
59.04974121466681,77.634182511677864
57.788223993230673,99.051414841748269
54.282328705967409,79.120646274680027
51.088719898979143,69.588897851118475
50.282836348230731,69.510503311494389
44.211741752090113,73.687564318317285
38.005488008060688,61.366904537240131
32.940479942618296,67.170655768995118
53.691639571070056,85.668203145001542
68.76573426962166,114.85387123391394
46.230966498310252,90.123572069967423
68.319360818255362,97.919821035242848
50.030174340312143,81.536990783015028
49.239765342753763,72.111832469615663
50.039575939875988,85.232007342325673
48.149858891028863,66.224957888054632
25.128484647772304,53.454394214850524