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：

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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

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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

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------------------------------- 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]]