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Gradient Boosting Trees using Python
# =============
# Introduction
# =============
# I've been doing some data mining lately and specially looking into `Gradient
# Boosting Trees <http://en.wikipedia.org/wiki/Gradient_boosting>`_ since it is
# claimed that this is one of the techniques with best performance out of the
# box. In order to have a better understanding of the technique I've reproduced
# the example of section *10.14.1 California Housing* in the book `The Elements of Statistical Learning <http://www-stat.stanford.edu/~tibs/ElemStatLearn/>`_.
# Each point of this dataset represents the house value of a property with some
# attributes of that house. You can get the data and the description of those
# attributes from `here <http://lib.stat.cmu.edu/modules.php?op=modload&name=Downloads&file=index&req=getit&lid=83>`_.
# I know that the whole exercise here can be easily done with the **R** package
# `gbm <http://cran.r-project.org/web/packages/gbm/index.html>`_ but I wanted to
# do the exercise using Python. Since learning several languages well enough is
# difficult and time consuming I would prefer to stick all my data analysis to
# Python instead doing it in R, even with R being superior on some cases. But
# having only one language for doing all your scripting, systems programming and
# prototyping *PLUS* your data analysis is a good reason for me. Your upfront
# effort of learning the language, setting up your tools and editors, etc. is
# done only once instead of twice.
#
# Data Preparation
# -----------------
# The first thing to do is to load the data into a `Pandas <http://pandas.pydata.org/pandas-docs/stable/>`_ dataframe
import numpy as np
import pandas as pd
columnNames = ['HouseVal','MedInc','HouseAge','AveRooms',
'AveBedrms','Population','AveOccup','Latitude','Longitud']
df = pd.read_csv('cadata.txt',skiprows=27, sep='\s+',names=columnNames)
# Now we have to split the datasets into training and validation. The training
# data will be used to generate the trees that will constitute the final
# averaged model.
import random
X = df[df.columns - ['HouseVal']]
Y = df['HouseVal']
rows = random.sample(df.index, int(len(df)*.80))
x_train, y_train = X.ix[rows],Y.ix[rows]
x_test,y_test = X.drop(rows),Y.drop(rows)
# We then fit a Gradient Tree Boosting model to the data using the
# `scikit-learn <http://scikit-learn.org/stable/>`_ package. We will use 500 trees
# with each tree having a depth of 6 levels. In order to get results similar to
# those in the book we also use the `Huber loss function <http://en.wikipedia.org/wiki/Huber_loss_function>`_ .
from sklearn.metrics import mean_squared_error,r2_score
from sklearn.ensemble import GradientBoostingRegressor
params = {'n_estimators': 500, 'max_depth': 6,
'learning_rate': 0.1, 'loss': 'huber','alpha':0.95}
clf = GradientBoostingRegressor(**params).fit(x_train, y_train)
# For me, the Mean Squared Error wasn't much informative and used instead the
# :math:`R^2` **coefficient of determination**. This measure is a number
# indicating how well a variable is able to predict the other. Numbers close to
# 0 means poor prediction and numbers close to 1 means perfect prediction. In the
# book, they claim a 0.84 against a 0.86 reported in the paper that created the
# dataset using a highly tuned algorithm. I'm getting a good 0.83 without much
# tunning of the parameters so it's a good out of the box technique.
mse = mean_squared_error(y_test, clf.predict(x_test))
r2 = r2_score(y_test, clf.predict(x_test))
print("MSE: %.4f" % mse)
print("R2: %.4f" % r2)
# Let's plot how does it behave the training and testing error
import matplotlib.pyplot as plt
# compute test set deviance
test_score = np.zeros((params['n_estimators'],), dtype=np.float64)
for i, y_pred in enumerate(clf.staged_decision_function(x_test)):
test_score[i] = clf.loss_(y_test, y_pred)
plt.figure(figsize=(12, 6))
plt.subplot(1, 1, 1)
plt.title('Deviance')
plt.plot(np.arange(params['n_estimators']) + 1, clf.train_score_, 'b-',
label='Training Set Deviance')
plt.plot(np.arange(params['n_estimators']) + 1, test_score, 'r-',
label='Test Set Deviance')
plt.legend(loc='upper right')
plt.xlabel('Boosting Iterations')
plt.ylabel('Deviance')
# As you can see in the previous graph, although the train error keeps going
# down as we add more trees to our model, the test error remains more or less
# constant and doesn't incur in overfitting. This is mainly due to the shrinkage
# parameter and one of the good features of this algorithm.
# When doing data mining as important as finding a good model is being able to
# interpret it, because based on that analysis and interpretation preemptive
# actions can be performed. Although base trees are easily interpretable when
# you are adding several of those trees interpretation is more difficult. You
# usually rely on some measures of the predictive power of each feature. Let's
# plot feature importance in predicting the House Value.
feature_importance = clf.feature_importances_
# make importances relative to max importance
feature_importance = 100.0 * (feature_importance / feature_importance.max())
sorted_idx = np.argsort(feature_importance)
pos = np.arange(sorted_idx.shape[0]) + .5
plt.figure(figsize=(12, 6))
plt.subplot(1, 1, 1)
plt.barh(pos, feature_importance[sorted_idx], align='center')
plt.yticks(pos, X.columns[sorted_idx])
plt.xlabel('Relative Importance')
plt.title('Variable Importance')
plt.show()
# Once variable importance has been identified we could try to investigate how
# those variables interact between them. For instance, we can plot the
# dependence of the target variable with another variable has been averaged over
# the values of the other variables not being taken into consideration. Some
# variables present a clear monotonic dependence with the target value, while
# others seem not very related to the target variable even when they ranked high
# in the previous plot. This could be signaling an interaction between variables
# that could be further studied.
from sklearn.ensemble.partial_dependence import plot_partial_dependence
fig, axs = plot_partial_dependence(clf, x_train,
features=[3,2,7,6],
feature_names=x_train.columns,
n_cols=2)
fig.show()
# The last step performed was to explore the capabilities of the Python
# libraries when plotting data in a map. Here we are plotting the predicted
# House Value in California using Latitude and Longitude as the axis for
# plotting this data in the map.
from mpl_toolkits.basemap import Basemap
predDf = pd.DataFrame(x_test.copy())
predDf['y_pred'] = clf.predict(x_test)
def california_map(ax=None, lllat=31.5,urlat=42.5,
lllon=-124,urlon=-113):
m = Basemap(ax=ax, projection='stere',
lon_0=(urlon + lllon) / 2,
lat_0=(urlat + lllat) / 2,
llcrnrlat=lllat, urcrnrlat=urlat,
llcrnrlon=lllon, urcrnrlon=urlon,
resolution='f')
m.drawstates()
m.drawcountries()
m.drawcoastlines(color='lightblue')
return m
plt.figure()
m= california_map()
predDf = predDf.sort('y_pred') # Useful for plotting
x,y = m(predDf['Longitud'],predDf['Latitude'])
serieA = (np.array(predDf['y_pred']) - predDf['y_pred'].min())/(predDf['y_pred'].max()-predDf['y_pred'].min())
# z = plt.cm.jet(serieA)
z = np.array(predDf['y_pred'])/1000
m.scatter(x,y,c=z,s=60,alpha=0.5,edgecolors='none')
c = m.colorbar(location='right')
c.set_label("House Value (Thousands of $)")
m.plot()
plt.show()
# Addendum
# --------
# This blog post was written using `Pylit <http://pylit.berlios.de/>`_ as the tool
# for doing `Literate Programming <http://en.wikipedia.org/wiki/Literate_programming>`_.
# I think that literate programming is way superior to other software
# methodologies like TDD when coding algorithms for data analysis. The main
# problem I find right now is the lack of tooling for really taking advantage of
# literate programming, but this is a technique that I'm definitely going to
# research deepe I think that literate programming is way superior to other
# software methodologies like TDD when coding algorithms for data analysis. The
# main problem I find right now is the lack of tooling for really taking
# advantage of literate programming, but this is a technique that I'm definitely
# going to research deeper.
@karthikziffer
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karthikziffer commented Dec 21, 2017

znelly , You can get the dataset from here . https://github.com/ppw123/cs686/blob/master/data/cadata.csv

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