From Scratch

In [26]:

    

import numpy as np
import matplotlib.pyplot as plt
import random
%matplotlib inline

N = 10
x = np.random.rand(N)
y = np.random.rand(N)

#plotting
plt.scatter(x,y)


    

    
Out[26]:





<matplotlib.collections.PathCollection at 0x11a8034e0>






    

In [27]:

    

#linear regression y = m*x + b
m = 0
b = 0

#implement using m = sum((x - x_mean)(y - y_mean)) / sum((x - x_mean)^2)
def lr(X, Y):
    global m,b
    x_mean = np.mean(X)
    y_mean = np.mean(Y)
    num = 0
    den = 0
    
    ## iterative
    #for x, y in zip(X, Y):
    #    num += (x - x_mean)*(y - y_mean)
    #    den += (x - x_mean)*(x - x_mean)
    
    ## vectorial
    num = sum((x -x_mean)*(y -y_mean))
    den = sum((x -x_mean)**2)
    
    m = num/den
    b = y_mean - (m * x_mean)

#calculate
lr(x, y)
print("m:{} b:{}".format(m, b))
plt.scatter(x, y)
plt.plot(x, m*x+b, 'r')


    

    




m:0.4969198614237362 b:0.1765862355572101






    
Out[27]:





[<matplotlib.lines.Line2D at 0x11a70cd68>]






    

In [28]:

    

#using linear regression formula: y = m*x + b

def gd(X, Y, lr, iterations=100):
    m = 0
    b = 0
    for i in range(iterations):
        m, b = step_gd(m, b, X, Y, lr)
        
    return m, b

#implement step gradient descent
def step_gd(m, b, X, Y, lr):
    m_grad = 0
    b_grad = 0
    for x, y in zip(X,Y):
        pred = m*x + b
        err = y - pred
        b_grad += err / len(X)
        m_grad += x * err / len(X)

    m += m_grad * lr
    b += b_grad * lr
    
    return m, b

#calculate
learning_rate = 0.1
m1, b1 = gd(x, y, learning_rate)
print("m1:{} b1:{}  (red)".format(m1, b1))

learning_rate = 0.5
m2, b2 = gd(x, y, learning_rate)
print("m2:{} b2:{}  (yellow)".format(m2, b2))

learning_rate = 1
m3, b3 = gd(x, y, learning_rate)
print("m3:{} b3:{}  (green)".format(m3, b3))

plt.scatter(x, y)
plt.plot(x, m1*x+b1, 'r')
plt.plot(x, m2*x+b2, 'y')
plt.plot(x, m3*x+b3, 'g')


    

    




m1:0.3323323939325161 b1:0.27020496356431617  (red)
m2:0.4824584674828272 b2:0.18481203178482208  (yellow)
m3:0.49628482485315994 b3:0.17694745118054395  (green)






    
Out[28]:





[<matplotlib.lines.Line2D at 0x11a9e1518>]