MLP实现波士顿房屋价格回归任务

1. 数据集

波士顿房屋价格.csv文件，文件中的数据有可能不完整，部分数据如下：

CRIM, ZN ,INDUS ,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,LSTAT,MEDV
0.00632,18,2.31,0,0.538,6.575,65.2,4.09,1,296,15.3,4.98,24
0.02731,0,7.07,0,0.469,6.421,78.9,4.9671,2,242,17.8,9.14,21.6
0.02729,0,7.07,0,0.469,7.185,61.1,4.9671,2,242,17.8,4.03,34.7
0.03237,0,2.18,0,0.458,6.998,45.8,6.0622,3,222,18.7,2.94,33.4
0.06905,0,2.18,0,0.458,7.147,54.2,6.0622,3,222,18.7,5.33,36.2
0.02985,0,2.18,0,0.458,6.43,58.7,6.0622,3,222,18.7,5.21,28.7
0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311,15.2,12.43,22.9
0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311,15.2,19.15,27.1
0.21124,12.5,7.87,0,0.524,5.631,100,6.0821,5,311,15.2,29.93,16.5
0.17004,12.5,7.87,0,0.524,6.004,85.9,6.5921,5,311,15.2,17.1,18.9
0.22489,12.5,7.87,0,0.524,6.377,94.3,6.3467,5,311,15.2,20.45,15
0.11747,12.5,7.87,0,0.524,6.009,82.9,6.2267,5,311,15.2,13.27,18.9
0.09378,12.5,7.87,0,0.524,5.889,39,5.4509,5,311,15.2,15.71,21.7
...

　　

2. 代码

import numpy as np

class MlpRegressor:
    def __init__(self, input_size, hidden_size1, hidden_size2, output_size, learning_rate=0.000001):
        self.input_size = input_size
        self.hidden_size1 = hidden_size1
        self.hidden_size2 = hidden_size2
        self.output_size = output_size
        self.learning_rate = learning_rate
        
        self.W1 = np.random.randn(input_size, hidden_size1) * 0.01
        self.b1 = np.zeros((1, hidden_size1))
        self.W2 = np.random.randn(hidden_size1, hidden_size2) * 0.01
        self.b2 = np.zeros((1, hidden_size2))
        self.W3 = np.random.randn(hidden_size2, output_size) * 0.01
        self.b3 = np.zeros((1, output_size))
    
    def relu(self, x):
        return np.maximum(x, 0)
    
    def relu_derivative(self, x):
        return np.where(x > 0, 1, 0)
    
    def forward(self, X):
        self.Z1 = np.dot(X, self.W1) + self.b1
        self.A1 = self.relu(self.Z1)
        self.Z2 = np.dot(self.A1, self.W2) + self.b2
        self.A2 = self.relu(self.Z2)
        self.Z3 = np.dot(self.A2, self.W3) + self.b3
        self.A3 = self.Z3
        return self.A3
    
    def backward(self, X, y):
        m = X.shape[0]
        dA3 = self.A3 - y
        dZ3 = dA3 * 1
        dW3 = np.dot(self.A2.T, dZ3) / m
        db3 = np.sum(dZ3, axis=0, keepdims=True) / m
        dA2 = np.dot(dZ3, self.W3.T)
        dZ2 = dA2 * self.relu_derivative(self.Z2)
        dW2 = np.dot(self.A1.T, dZ2) / m
        db2 = np.sum(dZ2, axis=0, keepdims=True) / m
        dA1 = np.dot(dZ2, self.W2.T)
        dZ1 = dA1 * self.relu_derivative(self.Z1)
        dW1 = np.dot(X.T, dZ1) / m
        db1 = np.sum(dZ1, axis=0, keepdims=True) / m
        
        # Update weights and biases
        self.W3 -= self.learning_rate * dW3
        self.b3 -= self.learning_rate * db3
        self.W2 -= self.learning_rate * dW2
        self.b2 -= self.learning_rate * db2
        self.W1 -= self.learning_rate * dW1
        self.b1 -= self.learning_rate * db1
    
    def train(self, X, y, epochs=100000, batch_size=64):
        m = X.shape[0]
        for epoch in range(epochs):
            for i in range(0, m, batch_size):
                X_batch = X[i:i+batch_size]
                y_batch = y[i:i+batch_size]
                
                # Forward propagation
                y_pred = self.forward(X_batch)
                
                # Backward propagation
                self.backward(X_batch, y_batch)
            
            if (epoch+1) % 1000 == 0:
                loss = np.mean((y - self.forward(X)) ** 2)
                print(f'Epoch {epoch+1}/{epochs}, Loss: {loss}')

    def predict(self, X):
        return self.forward(X)


if __name__ == '__main__':
    import pandas as pd
    from sklearn.model_selection import train_test_split

    # 从CSV文件加载数据
    data = pd.read_csv('C:\\Users\\zhang\\Desktop\\AI 框架\\作业\\第一次作业\\boston.csv')

    # 提取特征和目标变量
    X = data.drop('MEDV', axis=1)  # 特征
    y = data['MEDV']  # 目标变量

    # 划分训练集和测试集
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
    X_train = X_train.values.reshape(-1, 12) 
    y_train = y_train.values.reshape(-1, 1) 
    X_test = X_test.values.reshape(-1, 12)   
    y_test = y_test.values.reshape(-1, 1)   
    # 定义神经网络的参数
    input_size = X_train.shape[1]  # 输入层大小
    hidden_size1 = 64  # 隐藏层大小
    hidden_size2 = 32  # 隐藏层大小
    output_size = 1  # 输出层大小
    
    regressor_model = MlpRegressor(input_size, hidden_size1, hidden_size2, output_size) 
    regressor_model.train(X_train, y_train) 

    y_pred = regressor_model.predict(X_test)    
    print(y_pred)   

　　

3. 运行结果

------------------------------- Training ------------------------------- 
Epoch 1000/100000, Loss: 215.62193437067899
Epoch 2000/100000, Loss: 192.23747827864736
Epoch 3000/100000, Loss: 126.98647196839126
Epoch 4000/100000, Loss: 104.56790587428584
Epoch 5000/100000, Loss: 93.55895944555557
Epoch 6000/100000, Loss: 81.83677659220027
Epoch 7000/100000, Loss: 69.98101706862538
Epoch 8000/100000, Loss: 60.4438306323673
Epoch 9000/100000, Loss: 54.275051269137215
Epoch 10000/100000, Loss: 50.144528058278446
Epoch 11000/100000, Loss: 46.71168138687022
Epoch 12000/100000, Loss: 44.091385588842066
Epoch 13000/100000, Loss: 41.98703195048573
Epoch 14000/100000, Loss: 40.32358336326167
Epoch 15000/100000, Loss: 38.920320023943574
Epoch 16000/100000, Loss: 37.66334430017403
Epoch 17000/100000, Loss: 36.57507989257117
Epoch 18000/100000, Loss: 35.6136438473766
Epoch 19000/100000, Loss: 34.7649982576941
Epoch 20000/100000, Loss: 33.94940895608493
Epoch 21000/100000, Loss: 33.16146768674789
Epoch 22000/100000, Loss: 32.395166297024666
Epoch 23000/100000, Loss: 31.600705371799602
Epoch 24000/100000, Loss: 30.804917947962632
Epoch 25000/100000, Loss: 29.974635196398847
Epoch 26000/100000, Loss: 29.20624305663592
Epoch 27000/100000, Loss: 28.35745827864321
Epoch 28000/100000, Loss: 27.602636238259457
Epoch 29000/100000, Loss: 26.81650819310092
Epoch 30000/100000, Loss: 26.002914608193542
Epoch 31000/100000, Loss: 25.325440117147213
Epoch 32000/100000, Loss: 24.65334725693612
Epoch 33000/100000, Loss: 24.060109198505522
Epoch 34000/100000, Loss: 23.54033990229176
Epoch 35000/100000, Loss: 23.10805183197649
Epoch 36000/100000, Loss: 22.760178305933966
Epoch 37000/100000, Loss: 22.43516727905778
Epoch 38000/100000, Loss: 22.107765200437264
Epoch 39000/100000, Loss: 21.965537775136905
Epoch 40000/100000, Loss: 21.989661009199523
Epoch 41000/100000, Loss: 21.62034576184785
Epoch 42000/100000, Loss: 21.572752403139138
Epoch 43000/100000, Loss: 21.34211337200876
Epoch 44000/100000, Loss: 21.0702495450661
Epoch 45000/100000, Loss: 20.837503486889897
Epoch 46000/100000, Loss: 20.681326474362805
Epoch 47000/100000, Loss: 20.503454394563672
Epoch 48000/100000, Loss: 20.389419746474474
Epoch 49000/100000, Loss: 20.074870271025098
Epoch 50000/100000, Loss: 19.98878160482701
Epoch 51000/100000, Loss: 19.762006774714624
Epoch 52000/100000, Loss: 19.73720805461732
Epoch 53000/100000, Loss: 19.840507926145058
Epoch 54000/100000, Loss: 19.586065516878563
Epoch 55000/100000, Loss: 19.26826647737148
Epoch 56000/100000, Loss: 19.186796811752668
Epoch 57000/100000, Loss: 19.128833329447612
Epoch 58000/100000, Loss: 18.86699431502371
Epoch 59000/100000, Loss: 18.991072309691766
Epoch 60000/100000, Loss: 19.037016453401602
Epoch 61000/100000, Loss: 18.865622588128197
Epoch 62000/100000, Loss: 18.872795070321768
Epoch 63000/100000, Loss: 18.872594451190064
Epoch 64000/100000, Loss: 18.854228191893057
Epoch 65000/100000, Loss: 18.67904692926805
Epoch 66000/100000, Loss: 18.768560510204782
Epoch 67000/100000, Loss: 18.7118185353233
Epoch 68000/100000, Loss: 18.55438967997513
Epoch 69000/100000, Loss: 18.621562397315216
Epoch 70000/100000, Loss: 18.405648834715997
Epoch 71000/100000, Loss: 18.189924349964524
Epoch 72000/100000, Loss: 18.353894145904075
Epoch 73000/100000, Loss: 18.45440674353988
Epoch 74000/100000, Loss: 18.39953074149147
Epoch 75000/100000, Loss: 18.364700160941528
Epoch 76000/100000, Loss: 18.186265195636466
Epoch 77000/100000, Loss: 18.302174526166176
Epoch 78000/100000, Loss: 18.205052422317795
Epoch 79000/100000, Loss: 18.037575818441386
Epoch 80000/100000, Loss: 18.01479027887508
Epoch 81000/100000, Loss: 17.96447524097066
Epoch 82000/100000, Loss: 17.895826329884876
Epoch 83000/100000, Loss: 17.7832487773441
Epoch 84000/100000, Loss: 17.86057435108409
Epoch 85000/100000, Loss: 17.703615956724253
Epoch 86000/100000, Loss: 17.68351796915479
Epoch 87000/100000, Loss: 17.633931736731242
Epoch 88000/100000, Loss: 17.612497052225557
Epoch 89000/100000, Loss: 17.647989798918914
Epoch 90000/100000, Loss: 17.710895613739616
Epoch 91000/100000, Loss: 17.598476799927635
Epoch 92000/100000, Loss: 17.56779767441564
Epoch 93000/100000, Loss: 17.668065621304482
Epoch 94000/100000, Loss: 17.48657393624495
Epoch 95000/100000, Loss: 17.609330714804045
Epoch 96000/100000, Loss: 17.576140983650948
Epoch 97000/100000, Loss: 17.568941202807263
Epoch 98000/100000, Loss: 17.52902584563828
Epoch 99000/100000, Loss: 17.383449295966283
Epoch 100000/100000, Loss: 17.320131803597924

----------------------------- Prediction -----------------------------  
[[26.40028594]
 [35.95670906]
 [21.0375181 ]
 [26.81075528]
 [19.27303297]
 [19.24176243]
 [18.02909242]
 [18.33487919]
 [24.73263076]
 [18.90793689]
 [19.12267473]
 [17.93149187]
 [ 6.61505735]
 [20.76470599]
 [18.72246741]
 [30.04006402]
 [20.53259631]
 [10.52485402]
 [45.73780961]
 [18.29906554]
 [25.11074838]
 [26.06149324]
 [17.07979461]
 [22.89127798]
 [20.37305481]
 [15.75135761]
 [22.60178594]
 [18.58907094]
 [18.73504267]
 [18.63945006]
 [19.18184467]
 [24.63804329]
 [30.09810365]
 [28.96464891]
 [15.40000902]
 [19.41514728]
 [32.46295104]
 [22.51692248]
 [21.41680795]
 [26.37525141]
 [17.23718715]
 [34.40460321]
 [49.03923572]
 [20.31266774]
 [25.74679912]
 [18.24712181]
 [17.16189391]
 [27.57055882]
 [19.08726561]
 [31.30209539]
 [18.61876664]
 [33.61725349]
 [18.83749261]
 [28.45453076]
 [43.2806737 ]
 [28.16084359]
 [20.96559786]
 [36.19731044]
 [23.90688183]
 [17.84116438]
 [25.34401538]
 [32.92448779]
 [35.99460035]
 [21.36938789]
 [24.68693002]
 [16.16543793]
 [20.70512879]
 [25.19973729]
 [32.02685795]
 [16.72595575]
 [22.26460783]
 [34.84019666]
 [12.66375726]
 [23.07451255]
 [22.26649686]
 [ 8.78072356]
 [20.4205716 ]
 [46.24483168]
 [15.96989209]
 [15.28259261]
 [21.4773465 ]
 [13.02810024]
 [20.03181817]
 [11.16139533]
 [19.83595495]
 [29.22583834]
 [21.09276755]
 [26.42585934]
 [25.46828173]
 [20.37952764]
 [22.45176222]
 [ 9.03221341]
 [21.40233138]
 [19.99845823]
 [25.57073065]
 [22.63883292]
 [36.03449262]
 [ 9.66554266]
 [17.70571079]
 [16.65375084]
 [22.44931029]
 [23.52876957]]