Google TensorFlow课程 编程笔记（7）———稀疏性和 L1 正则化

学习目标：

• 计算模型大小
• 通过应用 L1 正则化来增加稀疏性，以减小模型大小

---

降低复杂性的一种方法是使用正则化函数，它会使权重正好为零。对于线性模型（例如线性回归），权重为零就相当于完全没有使用相应特征。除了可避免过拟合之外，生成的模型还会更加有效。

L1 正则化是一种增加稀疏性的好方法。

第1步：设置：加载必要的库+加载数据+数据预处理

from __future__ import print_function

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://dl.google.com/mlcc/mledu-datasets/california_housing_train.csv", sep=",")

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

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()
  # Create a boolean categorical feature representing whether the
  # medianHouseValue is above a set threshold.
  output_targets["median_house_value_is_high"] = (
    california_housing_dataframe["median_house_value"] > 265000).astype(float)
  return output_targets

 

第2步：预览检查数据

# 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())

 

第3步：创建输入函数

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

 

第4步：对数据进行分桶

def get_quantile_based_buckets(feature_values, num_buckets):
  quantiles = feature_values.quantile(
    [(i+1.)/(num_buckets + 1.) for i in range(num_buckets)])
  return [quantiles[q] for q in quantiles.keys()]

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

  Returns:
    A set of feature columns
  """

  bucketized_households = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("households"),
    boundaries=get_quantile_based_buckets(training_examples["households"], 10))
  bucketized_longitude = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("longitude"),
    boundaries=get_quantile_based_buckets(training_examples["longitude"], 50))
  bucketized_latitude = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("latitude"),
    boundaries=get_quantile_based_buckets(training_examples["latitude"], 50))
  bucketized_housing_median_age = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("housing_median_age"),
    boundaries=get_quantile_based_buckets(
      training_examples["housing_median_age"], 10))
  bucketized_total_rooms = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("total_rooms"),
    boundaries=get_quantile_based_buckets(training_examples["total_rooms"], 10))
  bucketized_total_bedrooms = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("total_bedrooms"),
    boundaries=get_quantile_based_buckets(training_examples["total_bedrooms"], 10))
  bucketized_population = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("population"),
    boundaries=get_quantile_based_buckets(training_examples["population"], 10))
  bucketized_median_income = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("median_income"),
    boundaries=get_quantile_based_buckets(training_examples["median_income"], 10))
  bucketized_rooms_per_person = tf.feature_column.bucketized_column(
    tf.feature_column.numeric_column("rooms_per_person"),
    boundaries=get_quantile_based_buckets(
      training_examples["rooms_per_person"], 10))

  long_x_lat = tf.feature_column.crossed_column(
    set([bucketized_longitude, bucketized_latitude]), hash_bucket_size=1000)

  feature_columns = set([
    long_x_lat,
    bucketized_longitude,
    bucketized_latitude,
    bucketized_housing_median_age,
    bucketized_total_rooms,
    bucketized_total_bedrooms,
    bucketized_population,
    bucketized_households,
    bucketized_median_income,
    bucketized_rooms_per_person])
  
  return feature_columns

 

第5步：计算模型大小

def model_size(estimator):
  variables = estimator.get_variable_names()
  size = 0
  for variable in variables:
    if not any(x in variable 
               for x in ['global_step',
                         'centered_bias_weight',
                         'bias_weight',
                         'Ftrl']
              ):
      size += np.count_nonzero(estimator.get_variable_value(variable))
  return size

 

第6步：构建训练模型

def train_linear_classifier_model(
    learning_rate,
    regularization_strength,
    steps,
    batch_size,
    feature_columns,
    training_examples,
    training_targets,
    validation_examples,
    validation_targets):

  periods = 7
  steps_per_period = steps / periods

  # Create a linear classifier object.
  """使用L1正则化"""
  my_optimizer = tf.train.FtrlOptimizer(learning_rate=learning_rate, l1_regularization_strength=regularization_strength)
  my_optimizer = tf.contrib.estimator.clip_gradients_by_norm(my_optimizer, 5.0)
  linear_classifier = tf.estimator.LinearClassifier(
      feature_columns=feature_columns,
      optimizer=my_optimizer
  )
  
  # Create input functions.
  training_input_fn = lambda: my_input_fn(training_examples, 
                                          training_targets["median_house_value_is_high"], 
                                          batch_size=batch_size)
  predict_training_input_fn = lambda: my_input_fn(training_examples, 
                                                  training_targets["median_house_value_is_high"], 
                                                  num_epochs=1, 
                                                  shuffle=False)
  predict_validation_input_fn = lambda: my_input_fn(validation_examples, 
                                                    validation_targets["median_house_value_is_high"], 
                                                    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("LogLoss (on validation data):")
  training_log_losses = []
  validation_log_losses = []
  for period in range (0, periods):
    # Train the model, starting from the prior state.
    linear_classifier.train(
        input_fn=training_input_fn,
        steps=steps_per_period
    )
    # Take a break and compute predictions.
    training_probabilities = linear_classifier.predict(input_fn=predict_training_input_fn)
    training_probabilities = np.array([item['probabilities'] for item in training_probabilities])
    
    validation_probabilities = linear_classifier.predict(input_fn=predict_validation_input_fn)
    validation_probabilities = np.array([item['probabilities'] for item in validation_probabilities])
    
    # Compute training and validation loss.
    training_log_loss = metrics.log_loss(training_targets, training_probabilities)
    validation_log_loss = metrics.log_loss(validation_targets, validation_probabilities)
    # Occasionally print the current loss.
    print("  period %02d : %0.2f" % (period, validation_log_loss))
    # Add the loss metrics from this period to our list.
    training_log_losses.append(training_log_loss)
    validation_log_losses.append(validation_log_loss)
  print("Model training finished.")

  # Output a graph of loss metrics over periods.
  plt.ylabel("LogLoss")
  plt.xlabel("Periods")
  plt.title("LogLoss vs. Periods")
  plt.tight_layout()
  plt.plot(training_log_losses, label="training")
  plt.plot(validation_log_losses, label="validation")
  plt.legend()

  return linear_classifier

 

第7步：先完全不用正则化看一下效果（做比对用）

即正则化强度设置为0.0

linear_classifier = train_linear_classifier_model(
    learning_rate=0.1,
    # TWEAK THE REGULARIZATION VALUE BELOW
    regularization_strength=0.0,
    steps=300,
    batch_size=100,
    feature_columns=construct_feature_columns(),
    training_examples=training_examples,
    training_targets=training_targets,
    validation_examples=validation_examples,
    validation_targets=validation_targets)
print("Model size:", model_size(linear_classifier))

 

第7步：使用用L1正则化

这里正则化强度设置为0.9，把模型大小控制为刚好小于600。

linear_classifier = train_linear_classifier_model(
    learning_rate=0.1,
    regularization_strength=0.9,
    steps=300,
    batch_size=100,
    feature_columns=construct_feature_columns(),
    training_examples=training_examples,
    training_targets=training_targets,
    validation_examples=validation_examples,
    validation_targets=validation_targets)
print("Model size:", model_size(linear_classifier))

这里可以明显看到不使用正则化的时候模型的大小的从783减少至549，将近三分之一，而模型的损失logloss则仅增加了0.01。可以看出L1正则化减少模型大小的效果时很显著的。而这里也有需要权衡的地方，正则化越强，我们获得的模型就越小，但会影响分类损失。

 

本文仅为个人学习笔记记录，请结合Google 机器学习，编程练习：稀疏性和 L1 正则化

编程练习地址：https://colab.research.google.com/notebooks/mlcc/sparsity_and_l1_regularization.ipynb?hl=zh-cn#scrollTo=hgGhy-okmkWL