#!/usr/bin/env python
# coding: utf-8

# Copyright (c) 2015, 2016 [Sebastian Raschka](sebastianraschka.com)
# 
# https://github.com/rasbt/python-machine-learning-book
# 
# [MIT License](https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt)

# # Python Machine Learning - Code Examples

# # Chapter 10 - Predicting Continuous Target Variables with Regression Analysis

# Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s).

# In[1]:


get_ipython().run_line_magic('load_ext', 'watermark')
get_ipython().run_line_magic('watermark', "-a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,sklearn,seaborn")


# *The use of `watermark` is optional. You can install this IPython extension via "`pip install watermark`". For more information, please see: https://github.com/rasbt/watermark.*

# <br>
# <br>

# ### Overview

# - [Introducing a simple linear regression model](#Introducing-a-simple-linear-regression-model)
# - [Exploring the Housing Dataset](#Exploring-the-Housing-Dataset)
#   - [Visualizing the important characteristics of a dataset](#Visualizing-the-important-characteristics-of-a-dataset)
# - [Implementing an ordinary least squares linear regression model](#Implementing-an-ordinary-least-squares-linear-regression-model)
#   - [Solving regression for regression parameters with gradient descent](#Solving-regression-for-regression-parameters-with-gradient-descent)
#   - [Estimating the coefficient of a regression model via scikit-learn](#Estimating-the-coefficient-of-a-regression-model-via-scikit-learn)
# - [Fitting a robust regression model using RANSAC](#Fitting-a-robust-regression-model-using-RANSAC)
# - [Evaluating the performance of linear regression models](#Evaluating-the-performance-of-linear-regression-models)
# - [Using regularized methods for regression](#Using-regularized-methods-for-regression)
# - [Turning a linear regression model into a curve - polynomial regression](#Turning-a-linear-regression-model-into-a-curve---polynomial-regression)
#   - [Modeling nonlinear relationships in the Housing Dataset](#Modeling-nonlinear-relationships-in-the-Housing-Dataset)
#   - [Dealing with nonlinear relationships using random forests](#Dealing-with-nonlinear-relationships-using-random-forests)
#     - [Decision tree regression](#Decision-tree-regression)
#     - [Random forest regression](#Random-forest-regression)
# - [Summary](#Summary)

# <br>
# <br>

# In[2]:


from IPython.display import Image
get_ipython().run_line_magic('matplotlib', 'inline')


# In[3]:


# Added version check for recent scikit-learn 0.18 checks
from distutils.version import LooseVersion as Version
from sklearn import __version__ as sklearn_version


# # Introducing a simple linear regression model

# In[4]:


Image(filename='./images/10_01.png', width=500) 


# <br>
# <br>

# # Exploring the Housing dataset

# Source: [https://archive.ics.uci.edu/ml/datasets/Housing](https://archive.ics.uci.edu/ml/datasets/Housing)
# 
# Attributes:
#     
# <pre>
# 1. CRIM      per capita crime rate by town
# 2. ZN        proportion of residential land zoned for lots over 
#                  25,000 sq.ft.
# 3. INDUS     proportion of non-retail business acres per town
# 4. CHAS      Charles River dummy variable (= 1 if tract bounds 
#                  river; 0 otherwise)
# 5. NOX       nitric oxides concentration (parts per 10 million)
# 6. RM        average number of rooms per dwelling
# 7. AGE       proportion of owner-occupied units built prior to 1940
# 8. DIS       weighted distances to five Boston employment centres
# 9. RAD       index of accessibility to radial highways
# 10. TAX      full-value property-tax rate per $10,000
# 11. PTRATIO  pupil-teacher ratio by town
# 12. B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks 
#                  by town
# 13. LSTAT    % lower status of the population
# 14. MEDV     Median value of owner-occupied homes in $1000's
# </pre>

# In[5]:


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()


# <hr>
# 
# ### Note:
# 
# 
# If the link to the Housing dataset provided above does not work for you, you can find a local copy in this repository at [./../datasets/housing/housing.data](./../datasets/housing/housing.data).
# 
# Or you could fetch it via

# In[6]:


df = pd.read_csv('https://raw.githubusercontent.com/rasbt/python-machine-learning-book/master/code/datasets/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()


# <br>
# <br>

# ## Visualizing the important characteristics of a dataset

# In[7]:


import matplotlib.pyplot as plt
import seaborn as sns


sns.set(style='whitegrid', context='notebook')
cols = ['LSTAT', 'INDUS', 'NOX', 'RM', 'MEDV']

sns.pairplot(df[cols], size=2.5)
plt.tight_layout()
# plt.savefig('./figures/scatter.png', dpi=300)
plt.show()


# In[8]:


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.tight_layout()
# plt.savefig('./figures/corr_mat.png', dpi=300)
plt.show()


# In[9]:


sns.reset_orig()
get_ipython().run_line_magic('matplotlib', 'inline')


# <br>
# <br>

# # Implementing an ordinary least squares linear regression model

# ...

# ## Solving regression for regression parameters with gradient descent

# In[10]:


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[11]:


X = df[['RM']].values
y = df['MEDV'].values


# In[12]:


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[:, np.newaxis]).flatten()


# In[13]:


lr = LinearRegressionGD()
lr.fit(X_std, y_std)


# In[14]:


plt.plot(range(1, lr.n_iter+1), lr.cost_)
plt.ylabel('SSE')
plt.xlabel('Epoch')
plt.tight_layout()
# plt.savefig('./figures/cost.png', dpi=300)
plt.show()


# In[15]:


def lin_regplot(X, y, model):
    plt.scatter(X, y, c='lightblue')
    plt.plot(X, model.predict(X), color='red', linewidth=2)    
    return 


# In[16]:


lin_regplot(X_std, y_std, lr)
plt.xlabel('Average number of rooms [RM] (standardized)')
plt.ylabel('Price in $1000\'s [MEDV] (standardized)')
plt.tight_layout()
# plt.savefig('./figures/gradient_fit.png', dpi=300)
plt.show()


# In[17]:


print('Slope: %.3f' % lr.w_[1])
print('Intercept: %.3f' % lr.w_[0])


# In[18]:


num_rooms_std = sc_x.transform(np.array([[5.0]]))
price_std = lr.predict(num_rooms_std)
print("Price in $1000's: %.3f" % sc_y.inverse_transform(price_std))


# <br>
# <br>

# ## Estimating the coefficient of a regression model via scikit-learn

# In[19]:


from sklearn.linear_model import LinearRegression


# In[20]:


slr = LinearRegression()
slr.fit(X, y)
y_pred = slr.predict(X)
print('Slope: %.3f' % slr.coef_[0])
print('Intercept: %.3f' % slr.intercept_)


# In[21]:


lin_regplot(X, y, slr)
plt.xlabel('Average number of rooms [RM]')
plt.ylabel('Price in $1000\'s [MEDV]')
plt.tight_layout()
# plt.savefig('./figures/scikit_lr_fit.png', dpi=300)
plt.show()


# **Normal Equations** alternative:

# In[22]:


# adding a column vector of "ones"
Xb = np.hstack((np.ones((X.shape[0], 1)), X))
w = np.zeros(X.shape[1])
z = np.linalg.inv(np.dot(Xb.T, Xb))
w = np.dot(z, np.dot(Xb.T, y))

print('Slope: %.3f' % w[1])
print('Intercept: %.3f' % w[0])


# <br>
# <br>

# # Fitting a robust regression model using RANSAC

# In[23]:


from sklearn.linear_model import RANSACRegressor

if Version(sklearn_version) < '0.18':
    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)
else:
    ransac = RANSACRegressor(LinearRegression(), 
                             max_trials=100, 
                             min_samples=50, 
                             loss='absolute_loss', 
                             residual_threshold=5.0, 
                             random_state=0)


ransac.fit(X, y)
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 [MEDV]')
plt.legend(loc='upper left')

plt.tight_layout()
# plt.savefig('./figures/ransac_fit.png', dpi=300)
plt.show()


# In[24]:


print('Slope: %.3f' % ransac.estimator_.coef_[0])
print('Intercept: %.3f' % ransac.estimator_.intercept_)


# <br>
# <br>

# # Evaluating the performance of linear regression models

# In[25]:


if Version(sklearn_version) < '0.18':
    from sklearn.cross_validation import train_test_split
else:
    from sklearn.model_selection 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)


# In[26]:


slr = LinearRegression()

slr.fit(X_train, y_train)
y_train_pred = slr.predict(X_train)
y_test_pred = slr.predict(X_test)


# In[27]:


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.tight_layout()

# plt.savefig('./figures/slr_residuals.png', dpi=300)
plt.show()


# In[28]:


from sklearn.metrics import r2_score
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)))
print('R^2 train: %.3f, test: %.3f' % (
        r2_score(y_train, y_train_pred),
        r2_score(y_test, y_test_pred)))


# <br>
# <br>

# # Using regularized methods for regression

# In[29]:


from sklearn.linear_model import Lasso

lasso = Lasso(alpha=0.1)
lasso.fit(X_train, y_train)
y_train_pred = lasso.predict(X_train)
y_test_pred = lasso.predict(X_test)
print(lasso.coef_)


# In[30]:


print('MSE train: %.3f, test: %.3f' % (
        mean_squared_error(y_train, y_train_pred),
        mean_squared_error(y_test, y_test_pred)))
print('R^2 train: %.3f, test: %.3f' % (
        r2_score(y_train, y_train_pred),
        r2_score(y_test, y_test_pred)))


# <br>
# <br>

# # Turning a linear regression model into a curve - polynomial regression

# In[31]:


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]

y = np.array([236.4, 234.4, 252.8, 
              298.6, 314.2, 342.2, 
              360.8, 368.0, 391.2,
              390.8])


# In[32]:


from sklearn.preprocessing import PolynomialFeatures

lr = LinearRegression()
pr = LinearRegression()
quadratic = PolynomialFeatures(degree=2)
X_quad = quadratic.fit_transform(X)


# In[33]:


# fit linear features
lr.fit(X, y)
X_fit = np.arange(250, 600, 10)[:, np.newaxis]
y_lin_fit = lr.predict(X_fit)

# fit quadratic features
pr.fit(X_quad, y)
y_quad_fit = pr.predict(quadratic.fit_transform(X_fit))

# plot results
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.tight_layout()
# plt.savefig('./figures/poly_example.png', dpi=300)
plt.show()


# In[34]:


y_lin_pred = lr.predict(X)
y_quad_pred = pr.predict(X_quad)


# In[35]:


print('Training MSE linear: %.3f, quadratic: %.3f' % (
        mean_squared_error(y, y_lin_pred),
        mean_squared_error(y, y_quad_pred)))
print('Training R^2 linear: %.3f, quadratic: %.3f' % (
        r2_score(y, y_lin_pred),
        r2_score(y, y_quad_pred)))


# <br>
# <br>

# ## Modeling nonlinear relationships in the Housing Dataset

# In[36]:


X = df[['LSTAT']].values
y = df['MEDV'].values

regr = LinearRegression()

# create quadratic features
quadratic = PolynomialFeatures(degree=2)
cubic = PolynomialFeatures(degree=3)
X_quad = quadratic.fit_transform(X)
X_cubic = cubic.fit_transform(X)

# fit features
X_fit = np.arange(X.min(), X.max(), 1)[:, np.newaxis]

regr = regr.fit(X, y)
y_lin_fit = regr.predict(X_fit)
linear_r2 = r2_score(y, regr.predict(X))

regr = regr.fit(X_quad, y)
y_quad_fit = regr.predict(quadratic.fit_transform(X_fit))
quadratic_r2 = r2_score(y, regr.predict(X_quad))

regr = regr.fit(X_cubic, y)
y_cubic_fit = regr.predict(cubic.fit_transform(X_fit))
cubic_r2 = r2_score(y, regr.predict(X_cubic))


# plot results
plt.scatter(X, y, label='training points', color='lightgray')

plt.plot(X_fit, y_lin_fit, 
         label='linear (d=1), $R^2=%.2f$' % linear_r2, 
         color='blue', 
         lw=2, 
         linestyle=':')

plt.plot(X_fit, y_quad_fit, 
         label='quadratic (d=2), $R^2=%.2f$' % quadratic_r2,
         color='red', 
         lw=2,
         linestyle='-')

plt.plot(X_fit, y_cubic_fit, 
         label='cubic (d=3), $R^2=%.2f$' % cubic_r2,
         color='green', 
         lw=2, 
         linestyle='--')

plt.xlabel('% lower status of the population [LSTAT]')
plt.ylabel('Price in $1000\'s [MEDV]')
plt.legend(loc='upper right')

plt.tight_layout()
# plt.savefig('./figures/polyhouse_example.png', dpi=300)
plt.show()


# Transforming the dataset:

# In[37]:


X = df[['LSTAT']].values
y = df['MEDV'].values

# transform features
X_log = np.log(X)
y_sqrt = np.sqrt(y)

# fit features
X_fit = np.arange(X_log.min()-1, X_log.max()+1, 1)[:, np.newaxis]

regr = regr.fit(X_log, y_sqrt)
y_lin_fit = regr.predict(X_fit)
linear_r2 = r2_score(y_sqrt, regr.predict(X_log))

# plot results
plt.scatter(X_log, y_sqrt, label='training points', color='lightgray')

plt.plot(X_fit, y_lin_fit, 
         label='linear (d=1), $R^2=%.2f$' % linear_r2, 
         color='blue', 
         lw=2)

plt.xlabel('log(% lower status of the population [LSTAT])')
plt.ylabel('$\sqrt{Price \; in \; \$1000\'s [MEDV]}$')
plt.legend(loc='lower left')

plt.tight_layout()
# plt.savefig('./figures/transform_example.png', dpi=300)
plt.show()


# <br>
# <br>

# # Dealing with nonlinear relationships using random forests

# ...

# ## Decision tree regression

# In[38]:


from sklearn.tree import DecisionTreeRegressor

X = df[['LSTAT']].values
y = df['MEDV'].values

tree = DecisionTreeRegressor(max_depth=3)
tree.fit(X, y)

sort_idx = X.flatten().argsort()

lin_regplot(X[sort_idx], y[sort_idx], tree)
plt.xlabel('% lower status of the population [LSTAT]')
plt.ylabel('Price in $1000\'s [MEDV]')
# plt.savefig('./figures/tree_regression.png', dpi=300)
plt.show()


# <br>
# <br>

# ## Random forest regression

# In[39]:


X = df.iloc[:, :-1].values
y = df['MEDV'].values

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.4, random_state=1)


# In[40]:


from sklearn.ensemble import RandomForestRegressor

forest = RandomForestRegressor(n_estimators=1000, 
                               criterion='mse', 
                               random_state=1, 
                               n_jobs=-1)
forest.fit(X_train, y_train)
y_train_pred = forest.predict(X_train)
y_test_pred = forest.predict(X_test)

print('MSE train: %.3f, test: %.3f' % (
        mean_squared_error(y_train, y_train_pred),
        mean_squared_error(y_test, y_test_pred)))
print('R^2 train: %.3f, test: %.3f' % (
        r2_score(y_train, y_train_pred),
        r2_score(y_test, y_test_pred)))


# In[41]:


plt.scatter(y_train_pred,  
            y_train_pred - y_train, 
            c='black', 
            marker='o', 
            s=35,
            alpha=0.5,
            label='Training data')
plt.scatter(y_test_pred,  
            y_test_pred - y_test, 
            c='lightgreen', 
            marker='s', 
            s=35,
            alpha=0.7,
            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.tight_layout()

# plt.savefig('./figures/slr_residuals.png', dpi=300)
plt.show()


# <br>
# <br>

# # Summary

# ...