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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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Learning Objectives:
Let's revisit our model from the previous First Steps with TensorFlow exercise.
First, we'll import the California housing data into a pandas DataFrame:
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from __future__ import print_function
import math
from IPython import display
from matplotlib import cm
from matplotlib import gridspec
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import sklearn.metrics as 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))
california_housing_dataframe["median_house_value"] /= 1000.0
california_housing_dataframe
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Next, we'll set up our input function, and define the function for model training:
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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(buffer_size=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, input_feature):
"""Trains a linear regression model.
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.
input_feature: A `string` specifying a column from `california_housing_dataframe`
to use as input feature.
Returns:
A Pandas `DataFrame` containing targets and the corresponding predictions done
after training the model.
"""
periods = 10
steps_per_period = steps / periods
my_feature = input_feature
my_feature_data = california_housing_dataframe[[my_feature]].astype('float32')
my_label = "median_house_value"
targets = california_housing_dataframe[my_label].astype('float32')
# Create input functions.
training_input_fn = lambda: my_input_fn(my_feature_data, targets, batch_size=batch_size)
predict_training_input_fn = lambda: my_input_fn(my_feature_data, targets, num_epochs=1, shuffle=False)
# Create feature columns.
feature_columns = [tf.feature_column.numeric_column(my_feature)]
# 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=feature_columns,
optimizer=my_optimizer
)
# Set up to plot the state of our model's line each period.
plt.figure(figsize=(15, 6))
plt.subplot(1, 2, 1)
plt.title("Learned Line by Period")
plt.ylabel(my_label)
plt.xlabel(my_feature)
sample = california_housing_dataframe.sample(n=300)
plt.scatter(sample[my_feature], sample[my_label])
colors = [cm.coolwarm(x) for x in np.linspace(-1, 1, periods)]
# 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):")
root_mean_squared_errors = []
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.
predictions = linear_regressor.predict(input_fn=predict_training_input_fn)
predictions = np.array([item['predictions'][0] for item in predictions])
# Compute loss.
root_mean_squared_error = math.sqrt(
metrics.mean_squared_error(predictions, targets))
# Occasionally print the current loss.
print(" period %02d : %0.2f" % (period, root_mean_squared_error))
# Add the loss metrics from this period to our list.
root_mean_squared_errors.append(root_mean_squared_error)
# Finally, track the weights and biases over time.
# Apply some math to ensure that the data and line are plotted neatly.
y_extents = np.array([0, sample[my_label].max()])
weight = linear_regressor.get_variable_value('linear/linear_model/%s/weights' % input_feature)[0]
bias = linear_regressor.get_variable_value('linear/linear_model/bias_weights')
x_extents = (y_extents - bias) / weight
x_extents = np.maximum(np.minimum(x_extents,
sample[my_feature].max()),
sample[my_feature].min())
y_extents = weight * x_extents + bias
plt.plot(x_extents, y_extents, color=colors[period])
print("Model training finished.")
# Output a graph of loss metrics over periods.
plt.subplot(1, 2, 2)
plt.ylabel('RMSE')
plt.xlabel('Periods')
plt.title("Root Mean Squared Error vs. Periods")
plt.tight_layout()
plt.plot(root_mean_squared_errors)
# Create a table with calibration data.
calibration_data = pd.DataFrame()
calibration_data["predictions"] = pd.Series(predictions)
calibration_data["targets"] = pd.Series(targets)
display.display(calibration_data.describe())
print("Final RMSE (on training data): %0.2f" % root_mean_squared_error)
return calibration_data
Both the total_rooms and population features count totals for a given city block.
But what if one city block were more densely populated than another? We can explore how block density relates to median house value by creating a synthetic feature that's a ratio of total_rooms and population.
In the cell below, create a feature called rooms_per_person, and use that as the input_feature to train_model().
What's the best performance you can get with this single feature by tweaking the learning rate? (The better the performance, the better your regression line should fit the data, and the lower the final RMSE should be.)
NOTE: You may find it helpful to add a few code cells below so you can try out several different learning rates and compare the results. To add a new code cell, hover your cursor directly below the center of this cell, and click CODE.
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#
# YOUR CODE HERE
#
california_housing_dataframe["rooms_per_person"] = (california_housing_dataframe["total_rooms"]/california_housing_dataframe["population"])
calibration_data = train_model(
learning_rate=0.00005,
steps=500,
batch_size=5,
input_feature="rooms_per_person"
)
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california_housing_dataframe["rooms_per_person"] = (
california_housing_dataframe["total_rooms"] / california_housing_dataframe["population"])
calibration_data = train_model(
learning_rate=0.05,
steps=500,
batch_size=5,
input_feature="rooms_per_person")
We can visualize the performance of our model by creating a scatter plot of predictions vs. target values. Ideally, these would lie on a perfectly correlated diagonal line.
Use Pyplot's scatter() to create a scatter plot of predictions vs. targets, using the rooms-per-person model you trained in Task 1.
Do you see any oddities? Trace these back to the source data by looking at the distribution of values in rooms_per_person.
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# YOUR CODE HERE
plt.figure(figsize=(15, 6))
plt.subplot(1, 2, 1)
plt.title("Outliers")
plt.ylabel("targets")
plt.xlabel("predictions")
plt.scatter(calibration_data["predictions"], calibration_data["targets"])
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plt.figure(figsize=(15, 6))
plt.subplot(1, 2, 1)
plt.scatter(calibration_data["predictions"], calibration_data["targets"])
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The calibration data shows most scatter points aligned to a line. The line is almost vertical, but we'll come back to that later. Right now let's focus on the ones that deviate from the line. We notice that they are relatively few in number.
If we plot a histogram of rooms_per_person, we find that we have a few outliers in our input data:
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plt.subplot(1, 2, 2)
_ = california_housing_dataframe["rooms_per_person"].hist()
See if you can further improve the model fit by setting the outlier values of rooms_per_person to some reasonable minimum or maximum.
For reference, here's a quick example of how to apply a function to a Pandas Series:
clipped_feature = my_dataframe["my_feature_name"].apply(lambda x: max(x, 0))
The above clipped_feature will have no values less than 0.
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# YOUR CODE HERE
california_housing_dataframe["rooms_per_person"] = (california_housing_dataframe["total_rooms"]/california_housing_dataframe["population"])
california_housing_dataframe["rooms_per_person"]= (california_housing_dataframe["rooms_per_person"]).apply(lambda x: max(x, 5))
_ = california_housing_dataframe["rooms_per_person"].hist()
calibration_data = train_model(
learning_rate=0.00005,
steps=500,
batch_size=5,
input_feature="rooms_per_person"
)
The histogram we created in Task 2 shows that the majority of values are less than 5. Let's clip rooms_per_person to 5, and plot a histogram to double-check the results.
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california_housing_dataframe["rooms_per_person"] = (
california_housing_dataframe["rooms_per_person"]).apply(lambda x: min(x, 5))
_ = california_housing_dataframe["rooms_per_person"].hist()
To verify that clipping worked, let's train again and print the calibration data once more:
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calibration_data = train_model(
learning_rate=0.05,
steps=500,
batch_size=5,
input_feature="rooms_per_person")
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_ = plt.scatter(calibration_data["predictions"], calibration_data["targets"])