Added a new example for 2d linear regression

rm TODO (which was done)

Author: yerdua1

examples/plot_2d_linear_regression.py

@@ -0,0 +1,107 @@
+"""
+===================================
+Linear regression in two dimensions
+===================================
+
+In this example, we try to predict the median price of houses in Boston's
+neighbors by looking at two features: the average of the number of rooms per
+dwelling and the pencentage of low status in the population.
+The linear regression is done using the `Boston Housing Dataset`_ which
+contains 13 features used to predict the median price of houses.
+The two features selected are the most efficent on the test set.
+The 3D representation allows a better understanding of the prediction
+mechanism with two features.
+
+This example is inspired by linear regression example from
+`scikit-learn documentation`_.
+
+.. _Boston Housing Dataset: https://www.kaggle.com/c/boston-housing
+.. _scikit-learn documentation: http://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html#sphx-glr-auto-examples-linear-model-plot-ols-py
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+from tick import linear_model
+from sklearn.metrics import mean_squared_error, r2_score
+from sklearn.utils import shuffle
+from sklearn.datasets import load_boston
+from mpl_toolkits.mplot3d import axes3d
+from matplotlib import cm
+
+# Load the Boston Housing Dataset
+features, label = load_boston(return_X_y=True)
+features, label = shuffle(features, label, random_state=0)
+
+# Use two features: the average of the number of rooms per dwelling and
+# the pencentage of low status of the population
+X = features[:, [5, 12]]
+
+# Split the data into training/testing sets
+n_train_data = int(0.8 * X.shape[0])
+
+X_train = X[:n_train_data]
+X_test = X[n_train_data:]
+
+y_train = label[:n_train_data]
+y_test = label[n_train_data:]
+
+# Create linear regression and fit it on the training set
+regr = linear_model.LinearRegression()
+regr.fit(X_train, y_train)
+
+# Make predictions using the testing set
+y_pred = regr.predict(X_test)
+
+print('Coefficients:')
+print(' intercept: {:.2f}'.format(regr.intercept))
+print(' average room per dwelling: {:.2f}'.format(regr.weights[0]))
+print(' percentage of low status in population: {:.2f}'
+      .format(regr.weights[1]))
+
+# The mean squared error
+print('Mean squared error on test set: {:.2f}'.format(
+    mean_squared_error(y_test, y_pred)))
+
+# Explained variance score: 1 is perfect prediction
+print('Variance score on test set: {:.2f}'.format(r2_score(y_test, y_pred)))
+# To work in 3D
+
+# We first generate a mesh grid
+resolution = 10
+x = X_test[:, 0]
+y = X_test[:, 1]
+z = y_test
+
+x_surf = np.linspace(min(x), max(x), resolution)
+y_surf = np.linspace(min(y), max(y), resolution)
+x_surf, y_surf = np.meshgrid(x_surf, y_surf)
+
+# and then predict the label for all values in the grid
+z_surf = np.zeros_like(x_surf)
+mesh_points = np.vstack((x_surf.ravel(), y_surf.ravel())).T
+z_surf.ravel()[:] = regr.predict(mesh_points)
+
+fig = plt.figure(figsize=(20, 5))
+
+# 3D representation under different rotated angles for a better visualazion
+xy_angles = [10, 35, 60, 85]
+z_angle = 20
+
+for i, angle in enumerate(xy_angles):
+    n_columns = len(xy_angles)
+    position = i + 1
+
+    ax = fig.add_subplot(1, n_columns, position, projection='3d')
+
+    ax.view_init(z_angle, angle)
+
+    ax.plot_surface(x_surf, y_surf, z_surf, cmap=cm.hot, rstride=1, cstride=1,
+                    alpha=0.3, linewidth=0.2, edgecolors='black')
+    ax.scatter(x, y, z)
+
+    ax.set_title('angle: {}°'.format(angle))
+    ax.set_zlabel('median house pricing')
+    ax.set_xlabel('avg room per dwelling')
+    ax.set_ylabel('% low status population')
+
+plt.show()