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

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import sklearn


# #Visualizing the dataset

# In[2]:


import scipy.io


# In[3]:


data = scipy.io.loadmat('ex5data1.mat')


# In[4]:


plt.figure(figsize=(8, 6))
plt.xlabel('Change in water level(x)')
plt.ylabel('Water flowing out of the dam(y)')
plt.scatter(data['X'], data['y'], c='r', marker='x')
plt.show()


# #Learning curve for linear regression

# In[5]:


from sklearn.learning_curve import learning_curve


# In[6]:


def plot_learning_curve(estimator, title, X, y, Xval, yval, xlim=None, ylim=None):
    iterations = range(2, len(X))
    train_error = []
    val_error = []
    for i in iterations:
        estimator.fit(X[:i], y[:i])
        train_error.append(100* (1 - estimator.score(X[:i], y[:i])))
        val_error.append(100 * (1- estimator.score(Xval, yval)))

    plt.figure(figsize=(8, 6))
    plt.title(title)
    plt.plot(iterations, train_error, label="Train")
    plt.plot(iterations, val_error, label="Cross Validation")
    plt.ylabel('Error (%)')
    plt.xlabel('Number of training examples')
    plt.xlim(xlim)
    plt.ylim(ylim)
    plt.legend()
    return plt


# In[7]:


from sklearn.linear_model import LinearRegression 
from sklearn.linear_model import Ridge


# In[8]:


clf = LinearRegression()
clf.fit(data['X'], data['y'])

print clf.coef_
print clf.intercept_


# In[9]:


plt.figure(figsize=(8, 6))
plt.xlabel('Change in water level(x)')
plt.ylabel('Water flowing out of the dam(y)')
plt.scatter(data['X'], data['y'], c='r', marker='x')
plt.plot(data['X'], clf.predict(data['X']))
plt.show()


# In[10]:


plot_learning_curve(clf, 'Learning curve for linear regression', data['X'], data['y'], data['Xval'], data['yval']).show()


# #Polynomial Regression Learning Curve

# ##$\lambda = 0$

# In[11]:


from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

clf2 = Pipeline([('poly', PolynomialFeatures(degree=6)),
                 ('zscore', StandardScaler()),
                 ('linear', Ridge(alpha=0.0))])
clf2.fit(data['X'], data['y'])


# In[12]:


plt.figure(figsize=(8, 6))
plt.xlabel('Change in water level(x)')
plt.ylabel('Water flowing out of the dam(y)')
plt.scatter(data['X'], data['y'], c='r', marker='x')
xx = np.linspace(-60, 50, 100)[:, np.newaxis]
plt.plot(xx, clf2.predict(xx))
plt.show()


# In[13]:


plot_learning_curve(clf2, 'Learning curve for polynomial regression', data['X'], data['y'], data['Xval'], data['yval']).show()


# ##$\lambda = 1$

# In[14]:


clf3 = Pipeline([('poly', PolynomialFeatures(degree=6)),
                 ('zscore', StandardScaler()),
                 ('linear', Ridge(alpha=1))])
clf3.fit(data['X'], data['y'])

print clf3.named_steps['linear'].coef_


# In[15]:


plt.figure(figsize=(8, 6))
plt.xlabel('Change in water level(x)')
plt.ylabel('Water flowing out of the dam(y)')
plt.scatter(data['X'], data['y'], c='r', marker='x')
xx = np.linspace(-60, 50, 100)[:, np.newaxis]
plt.plot(xx, clf3.predict(xx))
plt.show()


# In[16]:


plot_learning_curve(clf3, 'Learning curve for polynomial regression', data['X'], data['y'], data['Xval'], data['yval']).show()


# ##$\lambda = 100$

# In[17]:


clf4 = Pipeline([('poly', PolynomialFeatures(degree=6)),
                 ('zscore', StandardScaler()),
                 ('linear', Ridge(alpha=100))])
clf4.fit(data['X'], data['y'])

print clf4.named_steps['linear'].coef_


# In[18]:


plt.figure(figsize=(8, 6))
plt.xlabel('Change in water level(x)')
plt.ylabel('Water flowing out of the dam(y)')
plt.scatter(data['X'], data['y'], c='r', marker='x')
xx = np.linspace(-60, 50, 100)[:, np.newaxis]
plt.plot(xx, clf4.predict(xx))
plt.show()


# In[19]:


plot_learning_curve(clf4, 'Learning curve for polynomial regression', data['X'], data['y'], data['Xval'], data['yval']).show()


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