[机器学习速成课程]表示 (Representation)-学习笔记

设置

和之前一样，我们先加载并准备加利福尼亚州住房数据。

import math

from IPython import display
from matplotlib import cm
from matplotlib import gridspec
from matplotlib import pyplot as plt
import numpy as np
import pandas as pd
from sklearn import metrics
import tensorflow as tf
from tensorflow.python.data import Dataset

tf.logging.set_verbosity(tf.logging.ERROR)
pd.options.display.max_rows = 10
pd.options.display.float_format = '{:.1f}'.format

california_housing_dataframe = pd.read_csv("https://storage.googleapis.com/mledu-datasets/california_housing_train.csv", sep=",")

california_housing_dataframe = california_housing_dataframe.reindex(
    np.random.permutation(california_housing_dataframe.index))

和之前一样

def preprocess_features(california_housing_dataframe):
  """Prepares input features from California housing data set.

  Args:
    california_housing_dataframe: A Pandas DataFrame expected to contain data
      from the California housing data set.
  Returns:
    A DataFrame that contains the features to be used for the model, including
    synthetic features.
  """
  selected_features = california_housing_dataframe[
    ["latitude",
     "longitude",
     "housing_median_age",
     "total_rooms",
     "total_bedrooms",
     "population",
     "households",
     "median_income"]]
  processed_features = selected_features.copy()
  # Create a synthetic feature.
  processed_features["rooms_per_person"] = (
    california_housing_dataframe["total_rooms"] /
    california_housing_dataframe["population"])
  return processed_features

def preprocess_targets(california_housing_dataframe):
  """Prepares target features (i.e., labels) from California housing data set.

  Args:
    california_housing_dataframe: A Pandas DataFrame expected to contain data
      from the California housing data set.
  Returns:
    A DataFrame that contains the target feature.
  """
  output_targets = pd.DataFrame()
  # Scale the target to be in units of thousands of dollars.
  output_targets["median_house_value"] = (
    california_housing_dataframe["median_house_value"] / 1000.0)
  return output_targets

和之前一样

# Choose the first 12000 (out of 17000) examples for training.
training_examples = preprocess_features(california_housing_dataframe.head(12000))
training_targets = preprocess_targets(california_housing_dataframe.head(12000))

# Choose the last 5000 (out of 17000) examples for validation.
validation_examples = preprocess_features(california_housing_dataframe.tail(5000))
validation_targets = preprocess_targets(california_housing_dataframe.tail(5000))

# Double-check that we've done the right thing.
print "Training examples summary:"
display.display(training_examples.describe())
print "Validation examples summary:"
display.display(validation_examples.describe())

print "Training targets summary:"
display.display(training_targets.describe())
print "Validation targets summary:"
display.display(validation_targets.describe())

任务 1：构建良好的特征集

如果只使用 2 个或 3 个特征，您可以获得的最佳效果是什么？

相关矩阵展现了两两比较的相关性，既包括每个特征与目标特征之间的比较，也包括每个特征与其他特征之间的比较。

在这里，相关性被定义为皮尔逊相关系数。您不必理解具体数学原理也可完成本练习。

相关性值具有以下含义：

• -1.0：完全负相关
• 0.0：不相关
• 1.0：完全正相关

correlation_dataframe = training_examples.copy()
correlation_dataframe["target"] = training_targets["median_house_value"]

correlation_dataframe.corr()

与之前一样

def construct_feature_columns(input_features):
  """Construct the TensorFlow Feature Columns.

  Args:
    input_features: The names of the numerical input features to use.
  Returns:
    A set of feature columns
  """ 
  return set([tf.feature_column.numeric_column(my_feature)
              for my_feature in input_features])

与之前一样

def my_input_fn(features, targets, batch_size=1, shuffle=True, num_epochs=None):
    """Trains a linear regression model of one feature.
  
    Args:
      features: pandas DataFrame of features
      targets: pandas DataFrame of targets
      batch_size: Size of batches to be passed to the model
      shuffle: True or False. Whether to shuffle the data.
      num_epochs: Number of epochs for which data should be repeated. None = repeat indefinitely
    Returns:
      Tuple of (features, labels) for next data batch
    """
    
    # Convert pandas data into a dict of np arrays
    features = {key:np.array(value) for key,value in dict(features).items()}                                           
    
    # Construct a dataset, and configure batching/repeating
    ds = Dataset.from_tensor_slices((features,targets)) # warning: 2GB limit
    ds = ds.batch(batch_size).repeat(num_epochs)

    # Shuffle the data, if specified
    if shuffle:
      ds = ds.shuffle(10000)
    
    # Return the next batch of data
    features, labels = ds.make_one_shot_iterator().get_next()
    return features, labels

训练模型代码（与之前一样）：

def train_model(
    learning_rate,
    steps,
    batch_size,
    training_examples,
    training_targets,
    validation_examples,
    validation_targets):
  """Trains a linear regression model.
  
  In addition to training, this function also prints training progress information,
  as well as a plot of the training and validation loss over time.
  
  Args:
    learning_rate: A `float`, the learning rate.
    steps: A non-zero `int`, the total number of training steps. A training step
      consists of a forward and backward pass using a single batch.
    batch_size: A non-zero `int`, the batch size.
    training_examples: A `DataFrame` containing one or more columns from
      `california_housing_dataframe` to use as input features for training.
    training_targets: A `DataFrame` containing exactly one column from
      `california_housing_dataframe` to use as target for training.
    validation_examples: A `DataFrame` containing one or more columns from
      `california_housing_dataframe` to use as input features for validation.
    validation_targets: A `DataFrame` containing exactly one column from
      `california_housing_dataframe` to use as target for validation.
      
  Returns:
    A `LinearRegressor` object trained on the training data.
  """

  periods = 10
  steps_per_period = steps / periods

  # Create a linear regressor object.
  my_optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
  my_optimizer = tf.contrib.estimator.clip_gradients_by_norm(my_optimizer, 5.0)
  linear_regressor = tf.estimator.LinearRegressor(
      feature_columns=construct_feature_columns(training_examples),
      optimizer=my_optimizer
  )
    
  # Create input functions
  training_input_fn = lambda: my_input_fn(training_examples, 
                                          training_targets["median_house_value"], 
                                          batch_size=batch_size)
  predict_training_input_fn = lambda: my_input_fn(training_examples, 
                                                  training_targets["median_house_value"], 
                                                  num_epochs=1, 
                                                  shuffle=False)
  predict_validation_input_fn = lambda: my_input_fn(validation_examples, 
                                                    validation_targets["median_house_value"], 
                                                    num_epochs=1, 
                                                    shuffle=False)

  # Train the model, but do so inside a loop so that we can periodically assess
  # loss metrics.
  print "Training model..."
  print "RMSE (on training data):"
  training_rmse = []
  validation_rmse = []
  for period in range (0, periods):
    # Train the model, starting from the prior state.
    linear_regressor.train(
        input_fn=training_input_fn,
        steps=steps_per_period,
    )
    # Take a break and compute predictions.
    training_predictions = linear_regressor.predict(input_fn=predict_training_input_fn)
    training_predictions = np.array([item['predictions'][0] for item in training_predictions])
    
    validation_predictions = linear_regressor.predict(input_fn=predict_validation_input_fn)
    validation_predictions = np.array([item['predictions'][0] for item in validation_predictions])
    
    # Compute training and validation loss.
    training_root_mean_squared_error = math.sqrt(
        metrics.mean_squared_error(training_predictions, training_targets))
    validation_root_mean_squared_error = math.sqrt(
        metrics.mean_squared_error(validation_predictions, validation_targets))
    # Occasionally print the current loss.
    print "  period %02d : %0.2f" % (period, training_root_mean_squared_error)
    # Add the loss metrics from this period to our list.
    training_rmse.append(training_root_mean_squared_error)
    validation_rmse.append(validation_root_mean_squared_error)
  print "Model training finished."

  
  # Output a graph of loss metrics over periods.
  plt.ylabel("RMSE")
  plt.xlabel("Periods")
  plt.title("Root Mean Squared Error vs. Periods")
  plt.tight_layout()
  plt.plot(training_rmse, label="training")
  plt.plot(validation_rmse, label="validation")
  plt.legend()

  return linear_regressor

minimal_features = [
  "median_income",     #与target的皮尔森系数为0.7
  #"latitude",          #与target的皮尔森系数为-0.1
  "rooms_per_person"  #与target的皮尔森系数为0.2，为何添加rooms_per_person之后，RMSE period 09 : 165.48 增大。
                      #或者换个问法，为什么添加latitude为特征，RMSE会减少那么多?
]

minimal_training_examples = training_examples[minimal_features]
minimal_validation_examples = validation_examples[minimal_features]

_ = train_model(
    learning_rate=0.01,
    steps=500,
    batch_size=5,
    training_examples=minimal_training_examples,
    training_targets=training_targets,
    validation_examples=minimal_validation_examples,
    validation_targets=validation_targets)

任务 2：更好地利用纬度

绘制 latitude 与 median_house_value 的图形后，表明两者确实不存在线性关系。

不过，有几个峰值与洛杉矶和旧金山大致相对应。

plt.scatter(training_examples["latitude"], training_targets["median_house_value"])

尝试创建一些能够更好地利用纬度的合成特征。

例如，您可以创建某个特征，将 latitude 映射到值 |latitude - 38|，并将该特征命名为 distance_from_san_francisco。

或者，您可以将该空间分成 10 个不同的分桶（例如 latitude_32_to_33、latitude_33_to_34 等）：如果 latitude 位于相应分桶范围内，则显示值 1.0；如果不在范围内，则显示值 0.0。

使用相关矩阵来指导您构建合成特征；如果您发现效果还不错的合成特征，可以将其添加到您的模型中。

您可以获得的最佳验证效果是什么？

解决方案

除了 latitude 之外，我们还会保留 median_income，以便与之前的结果进行比较。

我们决定对纬度进行分桶。在 Pandas 中使用 Series.apply 执行此操作相当简单。

LATITUDE_RANGES = zip(xrange(32, 44), xrange(33, 45))
 # LATITUDE_RANGES :
 #[(32, 33),(33, 34),(34, 35),(35, 36),(36, 37),(37, 38),(38, 39),(39, 40),(40, 41),(41, 42),(42, 43),(43, 44)]
 # 如果样本的latitude位于纬度分桶（LATITUDE_RANGES）之中，则设置latitude_r[0]_to_r[1]的值为1，否则为0。
 # 例：latitude位32.5，则latitude_32_to_33：1，latitude_33_to_34：0，latitude_35_to_36：0……
 # r用来接收遍历LATITUDE_RANGES的元组。例：r[0]=32,r[1]=33
def select_and_transform_features(source_df):
  selected_examples = pd.DataFrame()
  selected_examples["median_income"] = source_df["median_income"]
  for r in LATITUDE_RANGES:
    selected_examples["latitude_%d_to_%d" % r] = source_df["latitude"].apply(
      lambda l: 1.0 if l >= r[0] and l < r[1] else 0.0)
  return selected_examples

selected_training_examples = select_and_transform_features(training_examples)
selected_validation_examples = select_and_transform_features(validation_examples)

selected_training_examples的值:

_ = train_model(
    learning_rate=0.01,
    steps=500,
    batch_size=5,
    training_examples=selected_training_examples,
    training_targets=training_targets,
    validation_examples=selected_validation_examples,
    validation_targets=validation_targets)

疑问:

1,为什么经过分桶处理之后的RMSE(period 09 : 140.27),比之前的(period 09 : 112.92)大?

如果分桶处理导致RMSE增大,那进行分桶处理的意义是什么?

自己认为的解答：本篇当中的分桶没有处理好。在下一篇「特征组合」中，当对多项属性进行分桶时，RMSE会下降（88.29）；当添加longtitude和latitude当特征组合，RMSE进一步下降（80.52）。分桶的意义：对属性进行分桶之后，在训练的过程中，每个分桶会得到自己的权重。

2,因为在洛杉矶和旧金山附近的latitude对应的median_house_value高(见下图),所以在这两座城市附近,可否认为latitude与median_house_value存在线性关系? 如果将这两座城市附近的分桶[(33,35),(37,39)]的值设置为1,其他为0,预测值是否会更准确?

自己认为当解答：如果我们只使用 latitude 特征进行学习，那么该模型可能会发现特定纬度（或特定纬度范围内，因为我们已经将其分桶）的城市街区更可能比其他街区住房成本高昂。longitude 特征的情况与此类似。但是，如果我们将 longitude 与 latitude 组合，产生的组合特征则代表一个明确的城市街区。如果模型发现某些城市街区（位于特定纬度和经度范围内）更可能比其他街区住房成本高昂，那么这将是比单独考虑两个特征更强烈的信号。如果我们组合 latitude 和 longitude 特征（例如，假设 longitude 被分到 2 个分桶中，而 latitude 有 3 个分桶），我们实际上会得到 6 个组合的二元特征。当我们训练模型时，每个特征都会分别获得自己的权重。