Notes

# imports
import numpy as np
import matplotlib.pyplot as plt
def generate_data_set(init_seed):

np.random.seed(init_seed)
x = np.random.rand(100, 1)
y = 2 + 3 * x + np.random.rand(100, 1)
return x, y

def predict(x, w):
return np.dot(x, w)
def cal_cost(theta,x,y):


m = len(y)

predictions = x.dot(theta)
cost = (1/2*m) * np.sum(np.square(predictions-y))
return cost
def fit_GD(x,y,theta,alpha,iterations):
'''
X = Matrix of X with added bias units
y = Vector of Y
theta=Vector of thetas np.random.randn(j,1)
learning_rate
iterations = no of iterations

Returns the final theta vector and array of cost history over no of iterations
'''
m = len(y)
cost_history = np.zeros(iterations)

for it in range(iterations):

prediction = np.dot(x,theta)

theta = theta -(1/m)*alpha*( x.T.dot((prediction - y)))

cost_history[it] = cal_cost(theta,x,y)

return theta, cost_history
fig,ax = plt.subplots(figsize=(12,8))

ax.set_ylabel('J(Theta)')
ax.set_xlabel('Iterations')
_=ax.plot(range(1000),cost_history,'b.')
m = x.shape[0]
x_train = np.c_[np.ones((m, 1)), x]
theta = np.random.randn(2,1)
# fit/train the model
w, cost_history = fit_GD(x_train,y,theta, 0.05, 1000)
print(w)