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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# https://www.apache.org/licenses/LICENSE-2.0
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Objectifs d'apprentissage :
Certaines fonctions de régularisation peuvent faire en sorte que des pondérations soient exactement égales à zéro. Il est donc judicieux d'utiliser une telle régularisation pour rendre les opérations moins complexes. Dans le cas des modèles linéaires, comme la régression, une pondération nulle équivaut à ne pas utiliser la caractéristique correspondante. Outre le fait que cela permet d'éviter le surapprentissage, le modèle obtenu s'avère plus efficace.
La régularisation L1 est un bon moyen d'augmenter la parcimonie.
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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://download.mlcc.google.com/mledu-datasets/california_housing_train.csv", sep=",")
california_housing_dataframe = california_housing_dataframe.reindex(
np.random.permutation(california_housing_dataframe.index))
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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
# median_house_value is above a set threshold.
output_targets["median_house_value_is_high"] = (
california_housing_dataframe["median_house_value"] > 265000).astype(float)
return output_targets
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# 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())
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def my_input_fn(features, targets, batch_size=1, shuffle=True, num_epochs=None):
"""Trains a linear regression model.
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
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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()]
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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
Pour calculer la taille du modèle, vous allez simplement compter le nombre de paramètres non nuls. Une fonction est mise à votre disposition pour vous faciliter la tâche. Cette fonction met en pratique une connaissance approfondie de l'API Estimators. N'essayez pas de comprendre comment elle fonctionne ; cela n'est pas nécessaire.
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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
Votre équipe doit construire un modèle de régression logistique très précis sur le SmartRing, un anneau tellement intelligent qu'il est capable de "détecter" les données démographiques d'un îlot urbain ('median_income', 'avg_rooms', 'households', etc.) et de vous dire s'il s'agit d'un quartier cher ou non.
Compte tenu de la petite taille du SmartRing, l'équipe d'ingénieurs a déterminé qu'il ne pouvait traiter qu'un modèle ne comportant pas plus de 600 paramètres. L'équipe en charge de la gestion des produits a, pour sa part, établi que le modèle ne pourrait pas être lancé tant que la perte logistique ne serait pas inférieure à 0,35 sur l'ensemble d'évaluation mis de côté.
Pouvez-vous utiliser votre arme secrète, à savoir la régularisation L1, pour optimiser le modèle afin qu'il réponde à la fois aux contraintes de taille et de justesse ?
Trouvez un paramètre d'intensité de régularisation L1 qui réponde aux deux contraintes, à savoir une taille de modèle inférieure à 600 et une perte logistique inférieure à 0,35 sur l'ensemble de validation.
Le code ci-dessous vous aidera à bien commencer. Vous pouvez appliquer la régularisation à votre modèle de différentes manières. Dans le cas présent, vous allez utiliser FtrlOptimizer, une classe conçue pour offrir de meilleurs résultats que la descente de gradient standard avec la régularisation L1.
Ici encore, l'entraînement du modèle est effectué sur l'intégralité de l'ensemble de données. Attendez-vous donc à ce qu'il s'exécute plus lentement que d'habitude.
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def train_linear_classifier_model(
learning_rate,
regularization_strength,
steps,
batch_size,
feature_columns,
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.
regularization_strength: A `float` that indicates the strength of the L1
regularization. A value of `0.0` means no regularization.
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.
feature_columns: A `set` specifying the input feature columns to use.
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 `LinearClassifier` object trained on the training data.
"""
periods = 7
steps_per_period = steps / periods
# Create a linear classifier object.
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
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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))
Une intensité de régularisation de 0,1 doit normalement suffire. Notez toutefois qu'il faut trouver un compromis : une régularisation plus poussée génère des modèles plus petits, mais risque d'affecter le coût de classification.
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linear_classifier = train_linear_classifier_model(
learning_rate=0.1,
regularization_strength=0.1,
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))