

In [1]:

    
%reload_ext autoreload
%autoreload 2
%matplotlib inline

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(context="notebook", style="darkgrid", palette="dark")

import sys
sys.path.append('..')

from helper import linear_regression as lr  # my own module
from helper import general as general



In [2]:

    
raw_data = pd.read_csv('ex1data2.txt', names=['square', 'bedrooms', 'price'])
raw_data.head()

1. normalize data



In [3]:

    
data = general.normalize_feature(raw_data)
data.head()

2. multi-var batch gradient decent



In [4]:

    
X = general.get_X(data)
print(X.shape, type(X))

y = general.get_y(data)
print(y.shape, type(y))









    



(47, 3) <class 'numpy.ndarray'>
(47,) <class 'numpy.ndarray'>



In [5]:

    
alpha = 0.01
theta = np.zeros(X.shape[1])
epoch = 500



In [6]:

    
final_theta, cost_data = lr.batch_gradient_decent(theta, X, y, epoch, alpha=alpha)



In [11]:

    
sns.tsplot(time=np.arange(len(cost_data)), data = cost_data)









    Out[11]:





<matplotlib.axes._subplots.AxesSubplot at 0x118cc1b00>



In [8]:

    
final_theta









    Out[8]:





array([ -1.22797753e-16,   8.30383883e-01,   8.23982853e-04])

3. learning rate



In [9]:

    
base = np.logspace(-1, -5, num=4)
candidate = np.sort(np.concatenate((base, base*3)))
print(candidate)









    



[  1.00000000e-05   3.00000000e-05   2.15443469e-04   6.46330407e-04
   4.64158883e-03   1.39247665e-02   1.00000000e-01   3.00000000e-01]



In [10]:

    
epoch=50

fig, ax = plt.subplots(figsize=(16, 9))

for alpha in candidate:
    _, cost_data = lr.batch_gradient_decent(theta, X, y, epoch, alpha=alpha)
    ax.plot(np.arange(epoch+1), cost_data, label=alpha)

ax.set_xlabel('epoch', fontsize=18)
ax.set_ylabel('cost', fontsize=18)
ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
ax.set_title('learning rate', fontsize=18)









    Out[10]:





<matplotlib.text.Text at 0x118a79390>

4. normal equation

this is fancy, but I don't see how this could help for non-convex optimization... so skip this one



In [ ]:

	square	bedrooms	price
0	2104	3	399900
1	1600	3	329900
2	2400	3	369000
3	1416	2	232000
4	3000	4	539900

	square	bedrooms	price
0	0.130010	-0.223675	0.475747
1	-0.504190	-0.223675	-0.084074
2	0.502476	-0.223675	0.228626
3	-0.735723	-1.537767	-0.867025
4	1.257476	1.090417	1.595389