def main():
# 2
data = np.genfromtxt('girls_age_weight_height_2_8.csv', delimiter=',')
lr = LinearRegression()
ones = np.ones(len(data))
x = np.array([ones, data[:,0], data[:,1]]).transpose()
y = data[:,2]
# 2.1
age_mean = np.mean(x[:,1])
age_std = np.std(x[:,1])
weight_mean = np.mean(x[:,2])
weight_std = np.std(x[:,2])
print "Feature 'age' - Mean: %f, STD: %f" % (age_mean, age_std)
print "Feature 'weight' - Mean: %f, STD: %f" % (weight_mean, weight_std)
x_scaled = np.array(x)
x_scaled[:,0] = ones
x_scaled[:,1] = (x[:,1] - age_mean)/age_std
x_scaled[:,2] = (x[:,2] - weight_mean)/weight_std
m, n = x.shape
# 2.3
alphas = [0.005, 0.001, 0.05, 0.1, 0.5, 1.0]
iterations_n = 50
iterations = np.arange(iterations_n)
risk = np.zeros(shape = (iterations_n, len(alphas))).T
for alpha_i in range(0, len(alphas)):
theta_sim = np.zeros(n)
for iteration_n in iterations:
theta_sim = lr.gradient_descent(x_scaled, y, theta_sim, alphas[alpha_i], iteration_n)
prediction = np.dot(x_scaled, theta_sim)
loss = prediction - y
risk[alpha_i][iteration_n] = lr.calculate_cost(loss, m)
for alpha_i in range(0, len(alphas)):
plt.plot(iterations, risk[alpha_i], label='Alpha: %f' % alphas[alpha_i])
theta = lr.gradient_descent(x_scaled,y,np.zeros(n), 1.0, iterations_n)
prediction = np.dot(x_scaled, theta)
point_to_guess = [1.0, (5.0-age_mean)/age_std, (20.0-weight_mean)/weight_std]
guess = np.sum(np.dot(theta, point_to_guess))
print "Betas: %s" % (theta)
print "The 5 year girl weighting 20 is approximately %f m tall." % (guess)
print "error %f" % lr.calculate_cost(prediction -y, m)
# 2.4
p = np.matrix(x)
theta = lr.normal_equation(p, y)
theta = np.ravel(theta)
guess = np.sum(np.dot(theta, [1.0, 5.0, 20.0]))
prediction = np.dot(x, theta.flatten())
print "Betas: %s" % (theta)
print "The 5 year girl weighting 20 is approximately %f m tall." % (guess)
print "error %f" % lr.calculate_cost(prediction - y, m)
plt.ylabel('Risk')
plt.xlabel('# of Iterations')
plt.legend()
plt.show()
def main():
# 1.1
data = np.genfromtxt('girls_train.csv', delimiter=',')
lr = LinearRegression()
ones = np.ones(len(data))
x = np.array([ones, data[:,0]]).transpose()
y = data[:,1]
plt.scatter(x[:,1], y)
plt.ylabel('Height')
plt.xlabel('Age')
# 1.2
m, n = x.shape
learning_rate = 0.05
number_of_iterations = 1500
theta = np.zeros(n)
theta = lr.gradient_descent(x, y, theta, learning_rate, number_of_iterations)
# 1.3
prediction = np.dot(x, theta)
plt.plot(x[:,1], prediction, label = "%fx + %f" % (theta[1], theta[0]))
plt.legend()
theta0_vals = np.linspace(-1.0, 1.0, 100)
theta1_vals = np.linspace(-1.0, 1.0, 100)
Z = np.zeros(shape=(theta0_vals.size, theta1_vals.size))
for t1, element in enumerate(theta0_vals):
for t2, element2 in enumerate(theta1_vals):
thetaT = np.zeros(shape=(2, 1))
thetaT[0][0] = element
thetaT[1][0] = element2
guess = np.dot(x, thetaT).flatten()
loss = guess - y
Z[t1, t2] = lr.calculate_cost(loss, m)
X, Y = np.meshgrid(theta0_vals, theta1_vals)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(X, Y, Z)
# 1.4
print "Model: %fx + %f" % (theta[1], theta[0])
print "Mean square error for training: %f" % lr.calculate_cost(prediction-y, m)
print "Predicted height for a 4.5 years old girl: %f" % (4.5*theta[1] + theta[0])
test_data = np.genfromtxt('girls_test.csv', delimiter=',')
test_x = np.array([np.ones(len(test_data)), test_data[:,0]]).transpose()
test_y = test_data[:,1]
test_prediction = np.dot(test_x, theta)
test_error = lr.calculate_cost(test_prediction - test_y, len(test_data))
print "Mean square error for testing: %f" % (test_error)
plt.show()
