在回归问题中，我们的目标是预测连续值的输出，如价格或概率。
我们采用了经典的Auto MPG数据集，并建立了一个模型来预测20世纪70年代末和80年代初汽车的燃油效率。 为此，我们将为该模型提供该时段内许多汽车的描述。 此描述包括以下属性：气缸，排量，马力和重量。
1.Auto MPG数据集
获取数据
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读取数据
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.数据预处理
清洗数据
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
划分训练集和测试集
train_dataset = dataset.sample(frac=0.8,random_state=0)
test_dataset = dataset.drop(train_dataset.index)
检测数据
观察训练集中几对列的联合分布。
sns.pairplot(train_dataset[["MPG", "Cylinders", "Displacement", "Weight"]], diag_kind="kde")
整体统计数据：
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
取出标签
train_labels = train_dataset.pop('MPG')
test_labels = test_dataset.pop('MPG')
标准化数据
最好使用不同比例和范围的特征进行标准化。 虽然模型可能在没有特征归一化的情况下收敛，但它使训练更加困难，并且它使得结果模型依赖于输入中使用的单位的选择。
def norm(x):
return (x - train_stats['mean']) / train_stats['std']
normed_train_data = norm(train_dataset)
normed_test_data = norm(test_dataset)
3.构建模型
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.训练模型
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)
.........................................................
测试
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.预测
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")