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@marcelcaraciolo
Created October 28, 2011 03:43
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linear regression
from numpy import loadtxt, zeros, ones, array, linspace, logspace
from pylab import scatter, show, title, xlabel, ylabel, plot, contour
#Evaluate the linear regression
def compute_cost(X, y, theta):
'''
Comput cost for linear regression
'''
#Number of training samples
m = y.size
predictions = X.dot(theta).flatten()
sqErrors = (predictions - y) ** 2
J = (1.0 / (2 * m)) * sqErrors.sum()
return J
def gradient_descent(X, y, theta, alpha, num_iters):
'''
Performs gradient descent to learn theta
by taking num_items gradient steps with learning
rate alpha
'''
m = y.size
J_history = zeros(shape=(num_iters, 1))
for i in range(num_iters):
predictions = X.dot(theta).flatten()
errors_x1 = (predictions - y) * X[:, 0]
errors_x2 = (predictions - y) * X[:, 1]
theta[0][0] = theta[0][0] - alpha * (1.0 / m) * errors_x1.sum()
theta[1][0] = theta[1][0] - alpha * (1.0 / m) * errors_x2.sum()
J_history[i, 0] = compute_cost(X, y, theta)
return theta, J_history
#Load the dataset
data = loadtxt('ex1data1.txt', delimiter=',')
#Plot the data
scatter(data[:, 0], data[:, 1], marker='o', c='b')
title('Profits distribution')
xlabel('Population of City in 10,000s')
ylabel('Profit in $10,000s')
#show()
X = data[:, 0]
y = data[:, 1]
#number of training samples
m = y.size
#Add a column of ones to X (interception data)
it = ones(shape=(m, 2))
it[:, 1] = X
#Initialize theta parameters
theta = zeros(shape=(2, 1))
#Some gradient descent settings
iterations = 1500
alpha = 0.01
#compute and display initial cost
print compute_cost(it, y, theta)
theta, J_history = gradient_descent(it, y, theta, alpha, iterations)
print theta
#Predict values for population sizes of 35,000 and 70,000
predict1 = array([1, 3.5]).dot(theta).flatten()
print 'For population = 35,000, we predict a profit of %f' % (predict1 * 10000)
predict2 = array([1, 7.0]).dot(theta).flatten()
print 'For population = 70,000, we predict a profit of %f' % (predict2 * 10000)
#Plot the results
result = it.dot(theta).flatten()
plot(data[:, 0], result)
show()
#Grid over which we will calculate J
theta0_vals = linspace(-10, 10, 100)
theta1_vals = linspace(-1, 4, 100)
#initialize J_vals to a matrix of 0's
J_vals = zeros(shape=(theta0_vals.size, theta1_vals.size))
#Fill out J_vals
for t1, element in enumerate(theta0_vals):
for t2, element2 in enumerate(theta1_vals):
thetaT = zeros(shape=(2, 1))
thetaT[0][0] = element
thetaT[1][0] = element2
J_vals[t1, t2] = compute_cost(it, y, thetaT)
#Contour plot
J_vals = J_vals.T
#Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
xlabel('theta_0')
ylabel('theta_1')
scatter(theta[0][0], theta[1][0])
show()
@NatigAli
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NatigAli commented Apr 2, 2017

I am confused about the 15th line of your code: sqErrors = (predictions - y) ** 2.
predictions has 1xm shape and since y is defined as data[:,1] its shape is mx1.
As a result (predictions - y) returns 3x3 matrix.

So shouldn't it be as sqErrors = (predictions - y.T) ** 2? Then you get 1xm array.

@seemun-yum
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A little late to the comments, anyone knows where to get the ex1data1.txt file? :(

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