Pytorch: 全連接神經網絡-解決 Boston 房價回歸問題

Copyright: Jingmin Wei, Pattern Recognition and Intelligent System, School of Artificial and Intelligence, Huazhong University of Science and Technology

Pytorch教程專欄鏈接

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文章目錄

• • • Pytorch: 全連接神經網絡-解決 Boston 房價回歸問題
    • • MLP 回歸模型
      • • 房價數據準備
        • 搭建網絡預測房價

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MLP 回歸模型

使用sklearn庫的fetch_california_housing()函數。數據集共包含20640個樣本，有8個自變量。

import numpy as np import pandas as pd from sklearn.preprocessing import StandardScaler from sklearn.model_selection import train_test_split from sklearn.metrics import mean_squared_error, mean_absolute_error from sklearn.datasets import fetch_california_housingimport torch import torch.nn as nn import torch.nn.functional as F from torch.optim import SGD import torch.utils.data as Data import matplotlib.pyplot as plt import seaborn as sns

房價數據準備

# 導入數據 housedata = fetch_california_housing() # 切分訓練集和測試集 X_train, X_test, y_train, y_test = train_test_split(housedata.data, housedata.target,test_size = 0.3, random_state = 42)

70% 訓練集，30%測試集。

X_train, X_test, y_train, y_test (array([[ 4.1312 , 35. , 5.88235294, ..., 2.98529412,33.93 , -118.02 ],[ 2.8631 , 20. , 4.40120968, ..., 2.0141129 ,32.79 , -117.09 ],[ 4.2026 , 24. , 5.61754386, ..., 2.56491228,34.59 , -120.14 ],...,[ 2.9344 , 36. , 3.98671727, ..., 3.33206831,34.03 , -118.38 ],[ 5.7192 , 15. , 6.39534884, ..., 3.17889088,37.58 , -121.96 ],[ 2.5755 , 52. , 3.40257649, ..., 2.10869565,37.77 , -122.42 ]]),array([[ 1.6812 , 25. , 4.19220056, ..., 3.87743733,36.06 , -119.01 ],[ 2.5313 , 30. , 5.03938356, ..., 2.67979452,35.14 , -119.46 ],[ 3.4801 , 52. , 3.97715472, ..., 1.36033229,37.8 , -122.44 ],...,[ 3.512 , 16. , 3.76228733, ..., 2.36956522,33.67 , -117.91 ],[ 3.65 , 10. , 5.50209205, ..., 3.54751943,37.82 , -121.28 ],[ 3.052 , 17. , 3.35578145, ..., 2.61499365,34.15 , -118.24 ]]),array([1.938, 1.697, 2.598, ..., 2.221, 2.835, 3.25 ]),array([0.477 , 0.458 , 5.00001, ..., 2.184 , 1.194 , 2.098 ])) # 數據標準化處理 scale = StandardScaler() X_train_s = scale.fit_transform(X_train) X_test_s = scale.transform(X_test) # 將訓練數據轉為數據表 housedatadf = pd.DataFrame(data=X_train_s, columns = housedata.feature_names) housedatadf['target'] = y_train housedatadf MedIncHouseAgeAveRoomsAveBedrmsPopulationAveOccupLatitudeLongitudetarget01234...1444314444144451444614447

0.133506	0.509357	0.181060	-0.273850	-0.184117	-0.010825	-0.805682	0.780934	1.93800
-0.532218	-0.679873	-0.422630	-0.047868	-0.376191	-0.089316	-1.339473	1.245270	1.69700
0.170990	-0.362745	0.073128	-0.242600	-0.611240	-0.044800	-0.496645	-0.277552	2.59800
-0.402916	-1.155565	0.175848	-0.008560	-0.987495	-0.075230	1.690024	-0.706938	1.36100
-0.299285	1.857152	-0.259598	-0.070993	0.086015	-0.066357	0.992350	-1.430902	5.00001
...	...	...	...	...	...	...	...	...
1.308827	0.509357	0.281603	-0.383849	-0.675265	-0.007030	-0.875918	0.810891	2.29200
-0.434100	0.350793	0.583037	0.383154	0.285105	0.063443	-0.763541	1.075513	0.97800
-0.494787	0.588640	-0.591570	-0.040978	0.287736	0.017201	-0.758858	0.601191	2.22100
0.967171	-1.076283	0.390149	-0.067164	0.306154	0.004821	0.903385	-1.186252	2.83500
-0.683202	1.857152	-0.829656	-0.087729	1.044630	-0.081672	0.992350	-1.415923	3.25000

14448 rows × 9 columns

使用相關系數熱力圖分析數據集中9個變量的相關性

datacor = np.corrcoef(housedatadf.values, rowvar=0) datacor = pd.DataFrame(data = datacor, columns = housedatadf.columns,index = housedatadf.columns) plt.figure(figsize=(8, 6)) ax = sns.heatmap(datacor, square = True, annot = True, fmt = '.3f',linewidths = .5, cmap = 'YlGnBu',cbar_kws = {'fraction': 0.046, 'pad': 0.03}) plt.show()

從圖像可以看出，和目標函數相關性最大的是MedInc(收入中位數)變量。而且AveRooms和AveBedrms兩個變量的正相關性較強。

# 將數據集轉為張量 X_train_t = torch.from_numpy(X_train_s.astype(np.float32)) y_train_t = torch.from_numpy(y_train.astype(np.float32)) X_test_t = torch.from_numpy(X_test_s.astype(np.float32)) y_test_t = torch.from_numpy(y_test.astype(np.float32)) # 將訓練數據處理為數據加載器 train_data = Data.TensorDataset(X_train_t, y_train_t) test_data = Data.TensorDataset(X_test_t, y_test_t) train_loader = Data.DataLoader(dataset = train_data, batch_size = 64, shuffle = True, num_workers = 1)

搭建網絡預測房價

# 搭建全連接神經網絡回歸 class MLPregression(nn.Module):def __init__(self):super(MLPregression, self).__init__()# 第一個隱含層self.hidden1 = nn.Linear(in_features=8, out_features=100, bias=True)# 第二個隱含層self.hidden2 = nn.Linear(100, 100)# 第三個隱含層self.hidden3 = nn.Linear(100, 50)# 回歸預測層self.predict = nn.Linear(50, 1)# 定義網絡前向傳播路徑def forward(self, x):x = F.relu(self.hidden1(x))x = F.relu(self.hidden2(x))x = F.relu(self.hidden3(x))output = self.predict(x)# 輸出一個一維向量return output[:, 0] # 輸出網絡結構 from torchsummary import summary testnet = MLPregression() summary(testnet, input_size=(1, 8)) # 表示1個樣本，每個樣本有8個特征 ----------------------------------------------------------------Layer (type) Output Shape Param # ================================================================Linear-1 [-1, 1, 100] 900Linear-2 [-1, 1, 100] 10,100Linear-3 [-1, 1, 50] 5,050Linear-4 [-1, 1, 1] 51 ================================================================ Total params: 16,101 Trainable params: 16,101 Non-trainable params: 0 ---------------------------------------------------------------- Input size (MB): 0.00 Forward/backward pass size (MB): 0.00 Params size (MB): 0.06 Estimated Total Size (MB): 0.06 ---------------------------------------------------------------- # 輸出網絡結構 from torchviz import make_dot testnet = MLPregression() x = torch.randn(1, 8).requires_grad_(True) y = testnet(x) myMLP_vis = make_dot(y, params=dict(list(testnet.named_parameters()) + [('x', x)])) myMLP_vis

然后使用訓練集對網絡進行訓練

# 定義優化器 optimizer = torch.optim.SGD(testnet.parameters(), lr = 0.01) loss_func = nn.MSELoss() # 均方根誤差損失函數 train_loss_all = []# 對模型迭代訓練，總共epoch輪 for epoch in range(30):train_loss = 0train_num = 0# 對訓練數據的加載器進行迭代計算for step, (b_x, b_y) in enumerate(train_loader):output = testnet(b_x) # MLP在訓練batch上的輸出loss = loss_func(output, b_y) # 均方根損失函數optimizer.zero_grad() # 每次迭代梯度初始化0loss.backward() # 反向傳播，計算梯度optimizer.step() # 使用梯度進行優化train_loss += loss.item() * b_x.size(0)train_num += b_x.size(0)train_loss_all.append(train_loss / train_num) # 可視化損失函數的變換情況 plt.figure(figsize = (8, 6)) plt.plot(train_loss_all, 'ro-', label = 'Train loss') plt.legend() plt.grid() plt.xlabel('epoch') plt.ylabel('Loss') plt.show()

對網絡預測，并使用平均絕對值誤差來表示預測效果

y_pre = testnet(X_test_t) y_pre = y_pre.data.numpy() mae = mean_absolute_error(y_test, y_pre) print('在測試集上的絕對值誤差為:', mae) 在測試集上的絕對值誤差為: 0.39334159455403034

真實集和預測值可視化，查看之間的差異

index = np.argsort(y_test) plt.figure(figsize=(8, 6)) plt.plot(np.arange(len(y_test)), y_test[index], 'r', label = 'Original Y') plt.scatter(np.arange(len(y_pre)), y_pre[index], s = 3, c = 'b', label = 'Prediction') plt.legend(loc = 'upper left') plt.grid() plt.xlabel('Index') plt.ylabel('Y') plt.show()

在測試集上，MLP回歸正確地預測處理原始數據的變化趨勢，但部分樣本的預測差異較大。

總結

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