In [1]:
import pandas as pd
df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data',
header=None, sep='\s+')
df.columns = ['CRIM', 'ZN', 'INDUS', 'CHAS',
'NOX', 'RM', 'AGE', 'DIS', 'RAD',
'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']
df.head()
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In [3]:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('ggplot')
import seaborn as sns
sns.set(style='whitegrid', context='notebook')
cols = ['LSTAT', 'INDUS', 'NOX', 'RM', 'MEDV']
sns.pairplot(df[cols], size=2.5)
plt.show()
In [4]:
import numpy as np
cm = np.corrcoef(df[cols].values.T)
sns.set(font_scale=1.5)
hm = sns.heatmap(cm,
cbar=True,
annot=True,
square=True,
fmt='.2f',
annot_kws={'size': 15},
yticklabels=cols,
xticklabels=cols)
plt.show()
In [5]:
class LinearRegressionGD(object):
def __init__(self, eta=0.001, n_iter=20):
self.eta = eta
self.n_iter = n_iter
def fit(self, X, y):
self.w_ = np.zeros(1 + X.shape[1])
self.cost_ = []
for i in range(self.n_iter):
output = self.net_input(X)
errors = (y - output)
self.w_[1:] += self.eta * X.T.dot(errors)
self.w_[0] += self.eta * errors.sum()
cost = (errors**2).sum() / 2.0
self.cost_.append(cost)
return self
def net_input(self, X):
return np.dot(X, self.w_[1:] + self.w_[0])
def predict(self, X):
return self.net_input(X)
In [6]:
X = df[['RM']].values
y = df['MEDV'].values
from sklearn.preprocessing import StandardScaler
sc_x = StandardScaler()
sc_y = StandardScaler()
X_std = sc_x.fit_transform(X)
y_std = sc_y.fit_transform(y)
lr = LinearRegressionGD()
lr.fit(X_std, y_std)
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In [7]:
plt.plot(range(1, lr.n_iter+1), lr.cost_)
plt.ylabel('SSE')
plt.xlabel('Epoch')
plt.show()
In [8]:
def lin_regplot(X, y, model):
plt.scatter(X, y, c='blue')
plt.plot(X, model.predict(X), color='red')
return None
In [9]:
lin_regplot(X_std, y_std, lr)
plt.xlabel('Avg number of rooms [RM] (standardized)')
plt.ylabel('Price in $1000\'s [MEDV] (standardized)')
plt.show()
In [11]:
num_rooms_std = sc_x.transform([5.0])
price_std = lr.predict(num_rooms_std)
print("Price in $1000's: %.3f" %\
sc_y.inverse_transform(price_std))
In [13]:
from sklearn.linear_model import LinearRegression
slr = LinearRegression()
slr.fit(X, y)
print('Slope: %.3f' %slr.coef_[0])
print('Intercept: %.3f' % slr.intercept_)
In [14]:
lin_regplot(X, y, slr)
plt.xlabel('Avg number of rooms [RM]')
plt.ylabel('Price in $1000\'s [MEDV]')
plt.show()
In [15]:
from sklearn.linear_model import RANSACRegressor
ransac = RANSACRegressor(LinearRegression(),
max_trials=100,
min_samples=50,
residual_metric=lambda x: np.sum(np.abs(x), axis=1),
residual_threshold=5.0,
random_state=0)
ransac.fit(X, y)
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In [16]:
inlier_mask = ransac.inlier_mask_
outlier_mask = np.logical_not(inlier_mask)
line_X = np.arange(3, 10, 1)
line_y_ransac = ransac.predict(line_X[:, np.newaxis])
plt.scatter(X[inlier_mask], y[inlier_mask],
c='blue', marker='o', label='Inliers')
plt.scatter(X[outlier_mask], y[outlier_mask],
c='lightgreen', marker='s', label='Outliers')
plt.plot(line_X, line_y_ransac, color='red')
plt.xlabel('Average number of rooms [RM]')
plt.ylabel('Price in $1000\'s [MDEV]')
plt.legend(loc='upper left')
plt.show()
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print('Slope: %.3f' % ransac.estimator_.coef_[0])
print('Intercept: %.3f' %ransac.estimator_.intercept_)
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from sklearn.cross_validation import train_test_split
X = df.iloc[:, :-1].values
y = df['MEDV'].values
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.3, random_state=0)
slr = LinearRegression()
slr.fit(X_train, y_train)
y_train_pred = slr.predict(X_train)
y_test_pred = slr.predict(X_test)
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# Plot some residuals to detect nonlinearity and outliers
plt.scatter(y_train_pred, y_train_pred - y_train,
c='blue', marker='o', label='Training data')
plt.scatter(y_test_pred, y_test_pred - y_test,
c='lightgreen', marker='s', label='Test data')
plt.xlabel('Predicted values')
plt.ylabel('Residuals')
plt.legend(loc='upper left')
plt.hlines(y=0, xmin=-10, xmax=50, lw=2, color='red')
plt.xlim([-10, 50])
plt.show()
In [22]:
from sklearn.metrics import mean_squared_error
print('MSE train: %.3f, test %.3f' % (
mean_squared_error(y_train, y_train_pred),
mean_squared_error(y_test, y_test_pred)))
# indicating our model is overfitting
In [23]:
from sklearn.metrics import r2_score
print('R^2 train: %.3f, test: %.3f' %
(r2_score(y_train, y_train_pred),
r2_score(y_test, y_test_pred)))
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# Polynomial
from sklearn.preprocessing import PolynomialFeatures
X = np.array([258.0, 270.0, 294.0,
320.0, 342.0, 368.0,
396.0, 446.0, 480.0,
586.0])[:, np.newaxis]
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y = np.array([236.4, 234.4, 252.8,
298.6, 314.2, 342.2,
360.8, 368.0, 391.2,
390.8])
lr = LinearRegression()
pr = LinearRegression()
quadratic = PolynomialFeatures(degree=2)
X_quad = quadratic.fit_transform(X)
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# Fit a simple linear regression model for comparison
lr.fit(X, y)
X_fit = np.arange(250, 600, 10)[:, np.newaxis]
y_lin_fit = lr.predict(X_fit)
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# Fit a multimple regression model on the transformed features
# For polynomial regression
pr.fit(X_quad, y)
y_quad_fit = pr.predict(quadratic.fit_transform(X_fit))
plt.scatter(X, y, label='training points')
plt.plot(X_fit, y_lin_fit,
label='linear fit', linestyle='--')
plt.plot(X_fit, y_quad_fit,
label='quadratic fit')
plt.legend(loc='upper left')
plt.show()
In [29]:
y_lin_pred = lr.predict(X)
y_quad_pred = pr.predict(X_quad)
print('Training MSE linear: %.3f, quadratic: %.3f' % (
mean_squared_error(y, y_lin_pred),
mean_squared_error(y, y_quad_pred)))
In [30]:
print('Training R^2 linear: %.3f, quadratic: %.3f' % (
r2_score(y, y_lin_pred),
r2_score(y, y_quad_pred)))
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