需要帮助验证谷歌/机器学习课程提供的数据

Question

在谷歌提供的机器学习课程介绍的梯度下降页面中提供了特征和相应的标签、MSE损失函数、初始数据集和结果。我很难验证他们的结果，我想知道是否有人可以协助确认我是否犯了错误，或者他们是否犯了错误。非常感谢任何帮助或反馈。

谢谢！

我有以下内容：

import pandas as pd
import numpy as np

data = [3.5, 18], [3.69, 15], [3.44, 18], [3.43, 16], [4.34, 15], [4.42, 14], [2.37, 24]
initial_data_df = pd.DataFrame(data,columns=['pounds','mpg'])

number_of_iterations = 6
weight = 0 # initialize weights
bias = 0 # initialize weights
weight_slope = 0
bias_slope = 0
final_results_df = pd.DataFrame()
learning_rate = 0.01

for i in range(number_of_iterations):
    loss = calculate_loss(initial_data_df,weight,bias)
    final_results_df = update_results(final_results_df,weight,bias,loss)
    weight_slope = find_weight_slope(initial_data_df,weight,bias)
    bias_slope = find_bias_slope(initial_data_df,weight,bias)
    weight = new_weight_update(weight,learning_rate,weight_slope)
    bias = new_bias_update(bias,learning_rate,bias_slope)
print(final_results_df)

def calculate_loss(df,weight,bias):
    loss_summation = []
    for i in range(0,len(df)):
        loss_summation.append((df['mpg'][i]-((weight*df['pounds'][i])+bias))**2)
    return (sum(loss_summation)//len(df))

def update_results(df,weight,bias,loss):
    if df.empty:
        df = pd.DataFrame([[weight,bias,loss]],columns=['weight','bias','loss'])
    else:
        df = pd.concat([df,pd.DataFrame([[weight,bias,loss]],columns=df.columns)])
    return df

def find_weight_slope(df,weight,bias):
    weight_update_summation = []
    for i in range(0,len(df)):
        wx_plus_b = (weight*df['pounds'][i])+bias
        wx_plus_b_minus_y = wx_plus_b-df['mpg'][i]
        weight_update_summation.append(2*(wx_plus_b_minus_y*df['pounds'][i]))
    return sum(weight_update_summation)//len(df)

def find_bias_slope(df,weight,bias):
    bias_update_summation = []
    for i in range(0,len(df)):
        wx_plus_b = (weight*df['pounds'][i])+bias
        wx_plus_b_minus_y = wx_plus_b-df['mpg'][i]
        bias_update_summation.append(2*wx_plus_b_minus_y)
    total_sum = sum(bias_update_summation)
    return total_sum//len(df)

def new_weight_update(old_weight,lr,slope):
    return old_weight-1*lr*slope

def new_bias_update(old_bias,lr,slope):
    return old_bias-1*lr*slope

其产量：

iter weight  bias   loss
0    0.00    0.00   303.0
0    1.20    0.35   170.0
0    2.06    0.60   102.0
0    2.67    0.79   67.0
0    3.10    0.93   50.0
0    3.41    1.04   41.0

这与网站上提供的解决方案不同：

Iteration   Weight  Bias    Loss (MSE)
1           0       0       303.71
2           1.2     0.34    170.67
3           2.75    0.59    67.3
4           3.17    0.72    50.63
5           3.47    0.82    42.1
6           3.68    0.9     37.74

Answer 1

所以我根据谷歌提供的AI聊天机器人的反馈对我的脚本做了一些细微的调整。见下图：

import pandas as pd
import numpy as np

def main():
    data = [3.5, 18], [3.69, 15], [3.44, 18], [3.43, 16], [4.34, 15], [4.42, 14], [2.37, 24]
    initial_data_df = pd.DataFrame(data,columns=['pounds','mpg'])

    number_of_iterations = 6
    weight = 0 # initialize weights
    bias = 0 # initialize weights
    weight_slope = 0
    bias_slope = 0
    final_results_df = pd.DataFrame()
    learning_rate = 0.01

    for i in range(number_of_iterations):
        loss = round(calculate_loss(initial_data_df,weight,bias),2)
        final_results_df = update_results(final_results_df,weight,bias,loss)
        weight_slope = find_weight_slope(initial_data_df,weight,bias)
        bias_slope = find_bias_slope(initial_data_df,weight,bias)
        weight = round(new_weight_update(weight,learning_rate,weight_slope),2)
        bias = round(new_bias_update(bias,learning_rate,bias_slope),2)
    print(final_results_df)

def calculate_loss(df,weight,bias):
    loss_summation = []
    for i in range(0,len(df)):
        loss_summation.append((df['mpg'][i]-((weight*df['pounds'][i])+bias))**2)
    return (sum(loss_summation)/len(df))

def update_results(df,weight,bias,loss):
    if df.empty:
        df = pd.DataFrame([[weight,bias,loss]],columns=['weight','bias','loss'])
    else:
        df = pd.concat([df,pd.DataFrame([[weight,bias,loss]],columns=df.columns)])
    return df

def find_weight_slope(df,weight,bias):
    slope = []
    for i in range(0,len(df)):
        predicted_mpg = (weight*df['pounds'][i])+bias   #   predicted_mpg = (weight * car_weight) + bias
        error = predicted_mpg-df['mpg'][i]
        slope.append(error*2*df['pounds'][i])
    return sum(slope)/len(df)

def find_bias_slope(df,weight,bias):
    slope = []
    for i in range(0,len(df)):
        predicted_mpg = (weight*df['pounds'][i])+bias   #   predicted_mpg = (weight * car_weight) + bias
        error = predicted_mpg-df['mpg'][i]
        slope.append(2*error)
    return sum(slope)/len(df)

def new_weight_update(old_weight,lr,slope):
    return old_weight-(lr*slope)

def new_bias_update(old_bias,lr,slope):
    return old_bias-(lr*slope)

if __name__=='__main__':
    main()

通过这些更改，我得到以下结果：

   weight  bias    loss
0    0.00  0.00  303.71
0    1.20  0.34  170.67
0    2.05  0.59  103.22
0    2.66  0.77   68.66
0    3.09  0.91   51.13
0    3.40  1.01   42.11

我提供了计算出的加权斜率以获得下一个更新的权重，这应该是第三次迭代权重值。

根据这些结果和文档，我得出的结论是，谷歌的示例结果对于梯度下降来说是不正确的。我希望这可以帮助某人......