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回归：预测燃油效率

在一个回归问题中，我们的目标是预测一个连续值的输出，比如价格或概率。这与一个分类问题形成对比，我们的目标是从一系列类中选择一个类（例如，一张图片包含一个苹果或一个橘子，识别图片中的水果）。

本笔记本使用经典的[auto-mpg]（

此示例使用“tf.keras”API，有关详细信息，请参阅[本指南]（

import pathlibimport matplotlib.pyplot as pltimport pandas as pdimport seaborn as snsimport kerasfrom keras import layers%matplotlib inline

The Auto MPG dataset

The dataset is available from the .

Get the data

First download the dataset.

dataset_path = keras.utils.get_file("auto-mpg.data", "https://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data")dataset_path

'C:\\Users\\YIUYE\\.keras\\datasets\\auto-mpg.data'

Import it using pandas

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()

Clean the data

The dataset contains a few unknown values.

dataset.isnull().sum()

MPG             0Cylinders       0Displacement    0Horsepower      6Weight          0Acceleration    0Model Year      0Origin          0dtype: int64

To keep this initial tutorial simple drop those rows.

dataset = dataset.dropna()

The "Origin" column is really categorical, not numeric. So convert that to a one-hot:

origin = dataset.pop('Origin')

dataset['USA'] = (origin == 1)*1.0dataset['Europe'] = (origin == 2)*1.0dataset['Japan'] = (origin == 3)*1.0dataset.tail()

现在将数据集拆分为一个训练集和一个测试集。

我们将在模型的最终评估中使用测试集。

train_dataset = dataset.sample(frac=0.8,random_state=0)test_dataset = dataset.drop(train_dataset.index)

sns.pairplot(train_dataset[[ "Cylinders", "Displacement", "Weight"]], diag_kind="kde")sns.set()

Also look at the overall statistics:

train_stats = train_dataset.describe()train_stats.pop("MPG")train_stats = train_stats.transpose()train_stats

Split features from labels

Separate the target value, or “label”, from the features. This label is the value that you will train the model to predict.

train_labels = train_dataset.pop('MPG')test_labels = test_dataset.pop('MPG')

Normalize the data

Look again at the train_stats block above and note how different the ranges of each feature are.

规范化使用不同尺度和范围的特征是一个很好的实践。虽然模型可能在没有特征规范化的情况下收敛，但它使训练变得更加困难，并且使生成的模型依赖于输入中使用的单元的选择。

注意：尽管我们有意只从训练数据集生成这些统计信息，但这些统计信息也将用于规范化测试数据集。我们需要这样做，以将测试数据集投影到模型所训练的相同分发中。

def norm(x):  return (x - train_stats['mean']) / train_stats['std']normed_train_data = norm(train_dataset)normed_test_data = norm(test_dataset)

def build_model():  model = keras.Sequential([    layers.Dense(64, activation=tf.nn.relu, input_shape=[len(train_dataset.keys())]),    layers.Dense(64, activation=tf.nn.relu),    layers.Dense(1)  ])  optimizer = keras.optimizers.RMSprop(0.001)  model.compile(loss='mean_squared_error',                optimizer=optimizer,                metrics=['mean_absolute_error', 'mean_squared_error'])  return model

model = build_model()

model.summary()

_________________________________________________________________Layer (type)                 Output Shape              Param #   =================================================================dense_10 (Dense)             (None, 64)                640       _________________________________________________________________dense_11 (Dense)             (None, 64)                4160      _________________________________________________________________dense_12 (Dense)             (None, 1)                 65        =================================================================Total params: 4,865Trainable params: 4,865Non-trainable params: 0_________________________________________________________________

Now try out the model. Take a batch of 10 examples from the training data and call model.predict on it.

example_batch = normed_train_data[:10]example_result = model.predict(example_batch)example_result

array([[-0.03468257],       [-0.01342154],       [-0.15384783],       [-0.18010283],       [ 0.03922582],       [-0.12172151],       [ 0.10603201],       [ 0.2442987 ],       [ 0.00099315],       [ 0.18530795]], dtype=float32)

It seems to be working, and it produces a result of the expected shape and type.

Train the model

Train the model for 1000 epochs, and record the training and validation accuracy in the history object.

# Display training progress by printing a single dot for each completed epochclass PrintDot(keras.callbacks.Callback):  def on_epoch_end(self, epoch, logs):    if epoch % 100 == 0: print('')    print('.', end='')EPOCHS = 1000history = 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.epochhist.tail()

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['mean_absolute_error'],           label='Train Error')  plt.plot(hist['epoch'], hist['val_mean_absolute_error'],           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['mean_squared_error'],           label='Train Error')  plt.plot(hist['epoch'], hist['val_mean_squared_error'],           label = 'Val Error')  plt.ylim([0,20])  plt.legend()  plt.show()plot_history(history)

此图显示在大约100个周期后，验证错误几乎没有改善，甚至恶化。让我们更新“model.fit”调用，以便在验证分数没有提高时自动停止培训。我们将使用一个早期的回调来测试每个时代的训练条件。如果一个设定的时间段没有显示出改善，那么自动停止训练。

model = build_model()# The patience parameter is the amount of epochs to check for improvementearly_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)

.................................................

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:  1.79 MPG

Make predictions

Finally, predict MPG values using data in the testing set:

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_labelsplt.hist(error, bins = 25)plt.xlabel("Prediction Error [MPG]")_ = plt.ylabel("Count")

它不是很高斯的，但是我们可以预期，因为样本的数量非常小。

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