Notes

# imports
import math
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets.samples_generator import make_regression
import pylab
from scipy import stats

def generate_data_set(init_seed):
""" Generates Random Data
Returns
-------
CS471: Machine Learning Page 3
x : array-like, shape = [m_samples, n_features]
Training samples
y : array-like, shape = [m_samples, n_target_values]
Target values
"""
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):
""" Predicts the value after the model has been trained.
Parameters
----------
x : array-like, shape = [m_samples, n_features]
Test samples
Returns
-------
Predicted values
"""
return np.dot(x, w)

def gradient_descent(X,y,L,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 = 0
c = 0
n = len(y)
cost_history = np.zeros(iterations)
theta_history = np.zeros([iterations,2])

for it in range(iterations):
Y_pred = m*X + c # The current predicted value of Y
cost = (1/n) * sum([val**2 for val in (y-Y_pred)])
#print ("iter %s | J: %.3f" % (iter, cost) )
D_m = (-2/n) * sum(X * (y - Y_pred)) # Derivative wrt m
D_c = (-2/n) * sum(y - Y_pred) # Derivative wrt c
m = m - L * D_m # Update m
c = c - L * D_c # Update c
theta_history[it,:] =c, m
cost_history[it] = cost

return theta_history, cost_history



# generate random data-set
x, y = generate_data_set(0)
#print("x:/n",x)
#print("y:/n",y)
m = x.shape[0]
#print(m)
#print("X-TRAIN:", x_train)
# fit/train the model
#x_train = np.c_[np.ones((len(x),1)),x]
theta_history, cost_history = gradient_descent(x,y,0.05,1000)



#print(theta_history)
#print("Cost History: ", cost_history)
theta1 = theta_history[-1][1]
theta0 = theta_history[-1][0]
y_predict = (x*theta1)+ theta0
#print(y, y_predict)


print("theta0: ",theta0)
print("ntheta1: ",theta1)

print('Final cost/MSE: {:0.3f}'.format(cost_history[-1]))
sq = math.sqrt(cost_history[-1])
print("Root Mean Sqaured Error:{:0.3f}".format(sq))


# plot

plt.xlabel('x')
plt.ylabel('y')
plt.plot(range(1000), cost_history)
plt.show()




plt.scatter(x, y)
plt.plot([min(x), max(x)], [min(y_predict), max(y_predict)], color='red') # regression line
plt.show()