數據來源kaggle,官網都有介紹。https://www.kaggle.com/c/boston-housing
from keras.datasets import boston_housing
(train_data,train_targets),(test_data,test_targets) = boston_housing.load_data()
#訓練集形狀:
print(train_data.shape)
#測試集形狀:
print(test_data.shape)
D:\ANACONDA\ana3.5.2\lib\site-packages\h5py\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
from ._conv import register_converters as _register_converters
Using TensorFlow backend.
(404, 13)
(102, 13)
訓練集404條,測試集102條;每條記錄13個數值特徵。
房價單位爲1000美元。
#房價數據,房價範圍在10,000到50,000。
train_targets
array([15.2, 42.3, 50. , 21.1, 17.7, 18.5, 11.3, 15.6, 15.6, 14.4, 12.1,
17.9, 23.1, 19.9, 15.7, 8.8, 50. , 22.5, 24.1, 27.5, 10.9, 30.8,
32.9, 24. , 18.5, 13.3, 22.9, 34.7, 16.6, 17.5, 22.3, 16.1, 14.9,
23.1, 34.9, 25. , 13.9, 13.1, 20.4, 20. , 15.2, 24.7, 22.2, 16.7,
12.7, 15.6, 18.4, 21. , 30.1, 15.1, 18.7, 9.6, 31.5, 24.8, 19.1,
22. , 14.5, 11. , 32. , 29.4, 20.3, 24.4, 14.6, 19.5, 14.1, 14.3,
15.6, 10.5, 6.3, 19.3, 19.3, 13.4, 36.4, 17.8, 13.5, 16.5, 8.3,
14.3, 16. , 13.4, 28.6, 43.5, 20.2, 22. , 23. , 20.7, 12.5, 48.5,
14.6, 13.4, 23.7, 50. , 21.7, 39.8, 38.7, 22.2, 34.9, 22.5, 31.1,
28.7, 46. , 41.7, 21. , 26.6, 15. , 24.4, 13.3, 21.2, 11.7, 21.7,
19.4, 50. , 22.8, 19.7, 24.7, 36.2, 14.2, 18.9, 18.3, 20.6, 24.6,
18.2, 8.7, 44. , 10.4, 13.2, 21.2, 37. , 30.7, 22.9, 20. , 19.3,
31.7, 32. , 23.1, 18.8, 10.9, 50. , 19.6, 5. , 14.4, 19.8, 13.8,
19.6, 23.9, 24.5, 25. , 19.9, 17.2, 24.6, 13.5, 26.6, 21.4, 11.9,
22.6, 19.6, 8.5, 23.7, 23.1, 22.4, 20.5, 23.6, 18.4, 35.2, 23.1,
27.9, 20.6, 23.7, 28. , 13.6, 27.1, 23.6, 20.6, 18.2, 21.7, 17.1,
8.4, 25.3, 13.8, 22.2, 18.4, 20.7, 31.6, 30.5, 20.3, 8.8, 19.2,
19.4, 23.1, 23. , 14.8, 48.8, 22.6, 33.4, 21.1, 13.6, 32.2, 13.1,
23.4, 18.9, 23.9, 11.8, 23.3, 22.8, 19.6, 16.7, 13.4, 22.2, 20.4,
21.8, 26.4, 14.9, 24.1, 23.8, 12.3, 29.1, 21. , 19.5, 23.3, 23.8,
17.8, 11.5, 21.7, 19.9, 25. , 33.4, 28.5, 21.4, 24.3, 27.5, 33.1,
16.2, 23.3, 48.3, 22.9, 22.8, 13.1, 12.7, 22.6, 15. , 15.3, 10.5,
24. , 18.5, 21.7, 19.5, 33.2, 23.2, 5. , 19.1, 12.7, 22.3, 10.2,
13.9, 16.3, 17. , 20.1, 29.9, 17.2, 37.3, 45.4, 17.8, 23.2, 29. ,
22. , 18. , 17.4, 34.6, 20.1, 25. , 15.6, 24.8, 28.2, 21.2, 21.4,
23.8, 31. , 26.2, 17.4, 37.9, 17.5, 20. , 8.3, 23.9, 8.4, 13.8,
7.2, 11.7, 17.1, 21.6, 50. , 16.1, 20.4, 20.6, 21.4, 20.6, 36.5,
8.5, 24.8, 10.8, 21.9, 17.3, 18.9, 36.2, 14.9, 18.2, 33.3, 21.8,
19.7, 31.6, 24.8, 19.4, 22.8, 7.5, 44.8, 16.8, 18.7, 50. , 50. ,
19.5, 20.1, 50. , 17.2, 20.8, 19.3, 41.3, 20.4, 20.5, 13.8, 16.5,
23.9, 20.6, 31.5, 23.3, 16.8, 14. , 33.8, 36.1, 12.8, 18.3, 18.7,
19.1, 29. , 30.1, 50. , 50. , 22. , 11.9, 37.6, 50. , 22.7, 20.8,
23.5, 27.9, 50. , 19.3, 23.9, 22.6, 15.2, 21.7, 19.2, 43.8, 20.3,
33.2, 19.9, 22.5, 32.7, 22. , 17.1, 19. , 15. , 16.1, 25.1, 23.7,
28.7, 37.2, 22.6, 16.4, 25. , 29.8, 22.1, 17.4, 18.1, 30.3, 17.5,
24.7, 12.6, 26.5, 28.7, 13.3, 10.4, 24.4, 23. , 20. , 17.8, 7. ,
11.8, 24.4, 13.8, 19.4, 25.2, 19.4, 19.4, 29.1])
數據預處理
因爲數據各個特徵取值範圍各不相同,不能直接送到神經網絡模型中進行處理。儘管網絡模型能適應數據的多樣性,但是相應的學習過程變得非常困難。一種常見的數據處理方法是特徵歸一化normalization—減均值除以標準差;數據0中心化,方差爲1.
mean = train_data.mean(axis=0)
train_data -= mean # 減去均值
std = train_data.std(axis=0) # 特徵標準差
train_data /= std
test_data -= mean #測試集處理:使用訓練集的均值和標準差;不用重新計算
test_data /= std
模型構建
由於數據集數據量過小,模型也不能太複雜,否則容易發生過擬合。
from keras import models
from keras import layers
def build_model():
model = models.Sequential()
model.add(layers.Dense(64, activation='relu',input_shape=(train_data.shape[1],)))
model.add(layers.Dense(64, activation='relu'))
model.add(layers.Dense(1))
model.compile(optimizer='rmsprop', loss='mse', metrics=['mae'])
return model
模型的最後一層只有一個神經元,沒有激活函數–相當於一個線性層。這種處理方法常用在單標量回歸問題中。使用激活函數將會限制輸出結果的範圍,比如使用sigmoid激活函數,輸出結果在0~1之間。這裏,因爲最後一層只是一個線性層,模型的輸出結果可能是任意值。
模型的損失函數爲mse均方誤差。監測的指標爲mean absolute error(MAE)平均絕對誤差—兩個結果之間差的絕對值。
K折交叉驗證
當調整模型參數時,爲了評估模型,我們通常將數據集分成訓練集和驗證集。但是當數據量過小時,驗證集數目也變得很小,導致驗證集上的評估結果相互之間差異性很大—與訓練集和測試集的劃分結果相關。評估結果可信度不高。
最好的評估方式是採用K折交叉驗證–將數據集分成K份(K=4或5),實例化K個模型,每個模型在K-1份數據上進行訓練,在1份數據上進行評估,最後用K次評估分數的平均值做最後的評估結果。
import numpy as np
k = 4
num_val_samples = len(train_data) // k
num_epochs = 100
all_scores = []
for i in range(k):
print('processing fold #',i)
val_data = train_data[i*num_val_samples : (i+1)*num_val_samples] # 劃分出驗證集部分
val_targets = train_targets[i*num_val_samples : (i+1)*num_val_samples]
partial_train_data = np.concatenate([train_data[:i*num_val_samples],train_data[(i+1)* num_val_samples:] ],axis=0) # 將訓練集拼接到一起
partial_train_targets = np.concatenate([train_targets[:i*num_val_samples],train_targets[(i+1)* num_val_samples:] ],axis=0)
model = build_model()
model.fit(partial_train_data,partial_train_targets,epochs=num_epochs,batch_size=16,verbose=0)#模型訓練silent模型
val_mse, val_mae = model.evaluate(val_data, val_targets, verbose=0) # 驗證集上評估
all_scores.append(val_mae)
processing fold # 0
processing fold # 1
processing fold # 2
processing fold # 3
#模型訓練
model = build_model()
model.fit(train_data, train_targets,epochs=80, batch_size=16, verbose=0)
test_mse_score, test_mae_score = model.evaluate(test_data, test_targets)
print(test_mse_score, test_mae_score)
102/102 [==============================] - 0s 538us/step
18.04363639681947 2.575085022870232
小結
迴歸問題:損失函數通常爲MSE均方誤差;
模型評估監測指標通常爲MAE(mean absolute error);
當數據取值範圍不一致時,需要對特徵進行預處理;
數據量小時,可以採用K折驗證來衡量模型;
數據量小時,模型複雜度也應該相應的簡單,可以避免模型過擬合。