在回歸問題中，我們的目標是預測連續值的輸出，如價格或概率。
我們采用了經典的Auto MPG數據集，並建立了一個模型來預測20世紀70年代末和80年代初汽車的燃油效率。 為此，我們將為該模型提供該時段內許多汽車的描述。 此描述包括以下屬性：氣缸，排量，馬力和重量。
1.Auto MPG數據集
獲取數據
dataset_path = keras.utils.get_file('auto-mpg.data',
'https://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data')
print(dataset_path)
Downloading data from https://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data
32768/30286 [================================] - 1s 25us/step
/home/czy/.keras/datasets/auto-mpg.data
使用pandas讀取數據
column_names = ['MPG','Cylinders','Displacement','Horsepower','Weight',
'Acceleration', 'Model Year', 'Origin']
raw_dataset = pd.read_csv(dataset_path, names=column_names,
na_values='?', comment='\t',
sep=' ', skipinitialspace=True)
dataset = raw_dataset.copy()
dataset.tail()
MPG Cylinders Displacement Horsepower Weight Acceleration Model Year Origin
393 27.0 4 140.0 86.0 2790.0 15.6 82 1
394 44.0 4 97.0 52.0 2130.0 24.6 82 2
395 32.0 4 135.0 84.0 2295.0 11.6 82 1
396 28.0 4 120.0 79.0 2625.0 18.6 82 1
397 31.0 4 119.0 82.0 2720.0 19.4 82 1
2.數據預處理
清洗數據
print(dataset.isna().sum())
dataset = dataset.dropna()
origin = dataset.pop('Origin')
dataset['USA'] = (origin == 1)*1.0
dataset['Europe'] = (origin == 2)*1.0
dataset['Japan'] = (origin == 3)*1.0
dataset.tail()
MPG 0
Cylinders 0
Displacement 0
Horsepower 6
Weight 0
Acceleration 0
Model Year 0
Origin 0
dtype: int64
MPG Cylinders Displacement Horsepower Weight Acceleration Model Year USA Europe Japan
393 27.0 4 140.0 86.0 2790.0 15.6 82 1.0 0.0 0.0
394 44.0 4 97.0 52.0 2130.0 24.6 82 0.0 1.0 0.0
395 32.0 4 135.0 84.0 2295.0 11.6 82 1.0 0.0 0.0
396 28.0 4 120.0 79.0 2625.0 18.6 82 1.0 0.0 0.0
397 31.0 4 119.0 82.0 2720.0 19.4 82 1.0 0.0 0.0
划分訓練集和測試集
train_dataset = dataset.sample(frac=0.8,random_state=0)
test_dataset = dataset.drop(train_dataset.index)
檢測數據
觀察訓練集中幾對列的聯合分布。
sns.pairplot(train_dataset[["MPG", "Cylinders", "Displacement", "Weight"]], diag_kind="kde")
整體統計數據：
train_stats = train_dataset.describe()
train_stats.pop("MPG")
train_stats = train_stats.transpose()
train_stats
count mean std min 25% 50% 75% max
Cylinders 314.0 5.477707 1.699788 3.0 4.00 4.0 8.00 8.0
Displacement 314.0 195.318471 104.331589 68.0 105.50 151.0 265.75 455.0
Horsepower 314.0 104.869427 38.096214 46.0 76.25 94.5 128.00 225.0
Weight 314.0 2990.251592 843.898596 1649.0 2256.50 2822.5 3608.00 5140.0
Acceleration 314.0 15.559236 2.789230 8.0 13.80 15.5 17.20 24.8
Model Year 314.0 75.898089 3.675642 70.0 73.00 76.0 79.00 82.0
USA 314.0 0.624204 0.485101 0.0 0.00 1.0 1.00 1.0
Europe 314.0 0.178344 0.383413 0.0 0.00 0.0 0.00 1.0
Japan 314.0 0.197452 0.398712 0.0 0.00 0.0 0.00 1.0
取出標簽
train_labels = train_dataset.pop('MPG')
test_labels = test_dataset.pop('MPG')
標准化數據
最好使用不同比例和范圍的特征進行標准化。 雖然模型可能在沒有特征歸一化的情況下收斂，但它使訓練更加困難，並且它使得結果模型依賴於輸入中使用的單位的選擇。
def norm(x):
return (x - train_stats['mean']) / train_stats['std']
normed_train_data = norm(train_dataset)
normed_test_data = norm(test_dataset)
3.構建模型
def build_model():
model = keras.Sequential([
layers.Dense(64, activation='relu', input_shape=[len(train_dataset.keys())]),
layers.Dense(64, activation='relu'),
layers.Dense(1)
])
optimizer = tf.keras.optimizers.RMSprop(0.001)
model.compile(loss='mse',
optimizer=optimizer,
metrics=['mae', 'mse'])
return model
model = build_model()
model.summary()
Model: "sequential"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
dense (Dense) (None, 64) 640
_________________________________________________________________
dense_1 (Dense) (None, 64) 4160
_________________________________________________________________
dense_2 (Dense) (None, 1) 65
=================================================================
Total params: 4,865
Trainable params: 4,865
Non-trainable params: 0
_________________________________________________________________
example_batch = normed_train_data[:10]
example_result = model.predict(example_batch)
example_result
array([[0.18062565],
[0.1714489 ],
[0.22555563],
[0.29366603],
[0.69764495],
[0.08851457],
[0.6851174 ],
[0.32245407],
[0.02959149],
[0.38945067]], dtype=float32)
4.訓練模型
class PrintDot(keras.callbacks.Callback):
def on_epoch_end(self, epoch, logs):
if epoch % 100 == 0: print('')
print('.', end='')
EPOCHS = 1000
history = model.fit(
normed_train_data, train_labels,
epochs=EPOCHS, validation_split = 0.2, verbose=0,
callbacks=[PrintDot()])
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hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
hist.tail()
loss mae mse val_loss val_mae val_mse epoch
995 2.191127 0.940755 2.191127 10.422818 2.594117 10.422818 995
996 2.113679 0.903680 2.113679 10.723925 2.631320 10.723926 996
997 2.517261 0.989557 2.517261 9.497868 2.379198 9.497869 997
998 2.250272 0.931618 2.250272 11.017041 2.658538 11.017041 998
999 1.976393 0.853547 1.976393 9.890977 2.491739 9.890977 999
def plot_history(history):
hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
plt.figure()
plt.xlabel('Epoch')
plt.ylabel('Mean Abs Error [MPG]')
plt.plot(hist['epoch'], hist['mae'],
label='Train Error')
plt.plot(hist['epoch'], hist['val_mae'],
label = 'Val Error')
plt.ylim([0,5])
plt.legend()
plt.figure()
plt.xlabel('Epoch')
plt.ylabel('Mean Square Error [$MPG^2$]')
plt.plot(hist['epoch'], hist['mse'],
label='Train Error')
plt.plot(hist['epoch'], hist['val_mse'],
label = 'Val Error')
plt.ylim([0,20])
plt.legend()
plt.show()
plot_history(history)
使用early stop
model = build_model()
early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=10)
history = model.fit(normed_train_data, train_labels, epochs=EPOCHS,
validation_split = 0.2, verbose=0, callbacks=[early_stop, PrintDot()])
plot_history(history)
.........................................................
測試
loss, mae, mse = model.evaluate(normed_test_data, test_labels, verbose=0)
print("Testing set Mean Abs Error: {:5.2f} MPG".format(mae))
Testing set Mean Abs Error: 1.85 MPG
5.預測
test_predictions = model.predict(normed_test_data).flatten()
plt.scatter(test_labels, test_predictions)
plt.xlabel('True Values [MPG]')
plt.ylabel('Predictions [MPG]')
plt.axis('equal')
plt.axis('square')
plt.xlim([0,plt.xlim()[1]])
plt.ylim([0,plt.ylim()[1]])
_ = plt.plot([-100, 100], [-100, 100])
error = test_predictions - test_labels
plt.hist(error, bins = 25)
plt.xlabel("Prediction Error [MPG]")
_ = plt.ylabel("Count")