在具有一个特征的线性回归中,梯度下降系数通过每次迭代而增加

您好,我正在学习一些机器学习算法,为了理解,我试图实现一种线性回归算法,其中一个特征是使用梯度下降法的残差平方和作为成本函数,如下所示:

我的伪代码:

 while not converge
     w <- w - step*gradient

python代码

import math
import numpy as num

def get_regression_predictions(input_feature, intercept, slope):
    predicted_output = [intercept + xi*slope for xi in input_feature]
    return(predicted_output)

def rss(input_feature, output, intercept,slope):
    return sum( [ ( output.iloc[i] - (intercept + slope*input_feature.iloc[i]) )**2 for i in range(len(output))])

def train(input_feature,output,intercept,slope):


    file = open("train.csv","w")
    file.write("ID,intercept,slope,RSS\n")
    i =0

    while True:

        print("RSS:",rss(input_feature, output, intercept,slope))
 file.write(str(i)+","+str(intercept)+","+str(slope)+","+str(rss(input_feature, output, intercept,slope))+"\n")
        i+=1

        gradient = [derivative(input_feature, output, intercept,slope,n) for n in range(0,2) ]

        step = 0.05
        intercept -= step*gradient[0]
        slope-= step*gradient[1]
    return intercept,slope 


 def derivative(input_feature, output, intercept,slope,n):
     if n==0:
         return sum( [ -2*(output.iloc[i] - (intercept + slope*input_feature.iloc[i])) for i in range(0,len(output))] ) 
     return sum( [  -2*(output.iloc[i] - (intercept + slope*input_feature.iloc[i]))*input_feature.iloc[i]  for i in range(0,len(output))] ) 

使用主程序:

import Linear as lin
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split




df = pd.read_csv("test2.csv")


train = df

lin.train(train["X"],train["Y"], 0, 0)

测试2。csv:

X,Y
0,1
1,3
2,7
3,13
4,21

ID,intercept,slope,RSS
0,0,0,669
1,4.5,14.0,3585.25
2,-7.25,-18.5,19714.3125
3,19.375,58.25,108855.953125

从数学上讲,我认为这没有任何意义,我多次查看自己的代码,我认为它是正确的,我在做其他错误的事情?