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# Licensed under the Apache License, Version 2.0 (the "License");
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Conjuntos de atributos

Objetivo de aprendizaje: crear un conjunto de atributos mínimo que se desempeñe tan bien como un conjunto de atributos más complejo

Hasta ahora, hemos ingresado en el modelo todos nuestros atributos. Los modelos con menos atributos usan menos recursos y son más fáciles de mantener. Veamos si podemos desarrollar un modelo con un conjunto mínimo de atributos de vivienda que se desempeñe tan bien como uno que usa todos los atributos del conjunto de datos.

Preparación

Al igual que antes, carguemos y preparemos los datos de viviendas en California.


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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()
  # 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

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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())

Tarea 1: Desarrolla un buen conjunto de atributos

¿Cuál es el mejor rendimiento que puedes obtener con solo 2 o 3 atributos?

Una matriz de correlaciones muestra correlaciones entre pares de atributos en comparación con el objetivo y para cada atributo en comparación con otros atributos.

Aquí, correlación se define como el coeficiente de correlación de Pearson. Para este ejercicio, no es necesario que comprendas los detalles matemáticos.

Los valores de correlación tienen los siguientes significados:

  • -1.0: correlación negativa perfecta
  • 0.0: no existe correlación
  • 1.0: correlación positiva perfecta

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

correlation_dataframe.corr()

Idealmente, quisiéramos tener atributos estrechamente correlacionados con el objetivo.

También quisiéramos tener atributos que no estuvieran tan estrechamente correlacionados entre sí, de manera que agreguen información independiente.

Usa esta información para probar quitar atributos. También puedes intentar desarrollar atributos sintéticos adicionales, como proporciones de dos atributos sin procesar.

Para facilitar el trabajo, incluimos el código de entrenamiento del ejercicio anterior.


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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])

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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 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

Dedica 5 minutos a buscar un buen conjunto de atributos y parámetros de entrenamiento. A continuación, comprueba la solución para ver cuáles elegimos nosotros. No olvides que los distintos atributos pueden requerir diferentes parámetros de aprendizaje.


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#
# Your code here: add your features of choice as a list of quoted strings.
#
minimal_features = [
]

assert minimal_features, "You must select at least one feature!"

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

#
# Don't forget to adjust these parameters.
#
train_model(
    learning_rate=0.001,
    steps=500,
    batch_size=5,
    training_examples=minimal_training_examples,
    training_targets=training_targets,
    validation_examples=minimal_validation_examples,
    validation_targets=validation_targets)

Solución

Haz clic más abajo para conocer la solución.


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minimal_features = [
  "median_income",
  "latitude",
]

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)

Tarea 2: Usa mejor la función de latitud

Al representar latitude frente a median_house_value, se evidencia que, en realidad, no hay una relación lineal.

En lugar de eso, hay algunos picos, que a grandes rasgos corresponden a Los Ángeles y San Francisco.


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

Prueba crear algunos atributos sintéticos que se desempeñen mejor con el atributo de latitud.

Por ejemplo, podrías tener un atributo que asigne latitude a un valor de |latitude - 38| y denominarla distance_from_san_francisco.

O bien, podrías dividir el espacio en 10 agrupamientos diferentes: latitude_32_to_33, latitude_33_to_34, etc., cada uno que muestre un valor de 1.0 si latitude está dentro del rango de ese agrupamiento y, de lo contrario, un valor de 0.0.

Usa la matriz de correlaciones como guía para el desarrollo y, a continuación, si encuentras algo que te pueda resultar útil, agrégalo a tu modelo.

¿Cuál es el mejor rendimiento de validación que puedes obtener?


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#
# YOUR CODE HERE: Train on a new data set that includes synthetic features based on latitude.
#

Solución

Haz clic más abajo para conocer la solución.

Además de latitude, también conservaremos median_income para realizar una comparación con los resultados anteriores.

Decidimos agrupar la latitud. Esto es bastante sencillo de hacer en Pandas a través de Series.apply.


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LATITUDE_RANGES = zip(range(32, 44), range(33, 45))

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)

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_ = 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)