def part1_1_2_a_ii():
x1 = np.random.uniform(0, 1, 30)
epsilon = np.random.normal(0, 0.07, 30)
y1 = (np.sin(2 * np.pi * x1)**2) + epsilon
model_d2 = lr.fit(x1, y1, 2)
model_d5 = lr.fit(x1, y1, 5)
model_d10 = lr.fit(x1, y1, 10)
model_d14 = lr.fit(x1, y1, 14)
model_d18 = lr.fit(x1, y1, 18)
x_axis1 = np.linspace(0, 1, num=1000)
# configuration of plot
plt.xlim(0, 1)
plt.ylim(-0.5, 1.5)
plt.xlabel('x')
plt.ylabel('y')
estimate_y2 = lr.estimate(lr.pl_featured(x_axis1, 2), model_d2)
l1, = plt.plot(x_axis1, estimate_y2, color='green', label='dimension 2')
plt.scatter(x1, y1)
# Place a legend to the right of this smaller subplot.
#plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
#plt.show()
estimate_y5 = lr.estimate(lr.pl_featured(x_axis1, 5), model_d5)
l2, = plt.plot(x_axis1, estimate_y5, color='blue', label='dimension 5')
#plt.scatter(x1, y1)
# Place a legend to the right of this smaller subplot.
#plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
#plt.show()
estimate_y10 = lr.estimate(lr.pl_featured(x_axis1, 10), model_d10)
l3, = plt.plot(x_axis1, estimate_y10, color='black', label='dimension 10')
#plt.scatter(x1, y1)
# Place a legend to the right of this smaller subplot.
#plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
#plt.show()
estimate_y14 = lr.estimate(lr.pl_featured(x_axis1, 14), model_d14)
l4, = plt.plot(x_axis1, estimate_y14, color='red', label='dimension 14')
#plt.scatter(x1, y1)
# Place a legend to the right of this smaller subplot.
#plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
#plt.show()
estimate_y18 = lr.estimate(lr.pl_featured(x_axis1, 18), model_d18)
l5, = plt.plot(x_axis1, estimate_y18, color='purple', label='dimension 18')
#plt.scatter(x1, y1)
# Place a legend to the right of this smaller subplot.
plt.legend(handles=[l1, l2, l3, l4, l5],
labels=['k=2', 'k=5', 'k=10', 'k=14', 'k=18'],
bbox_to_anchor=(1.13, 1.025),
loc='upper right')
plt.show()
def part1_1_1_c():
#calculate estimate value for different dimension
estimate_y1 = lr.estimate(lr.pl_featured(x, 1), model_d1)
estimate_y2 = lr.estimate(lr.pl_featured(x, 2), model_d2)
estimate_y3 = lr.estimate(lr.pl_featured(x, 3), model_d3)
estimate_y4 = lr.estimate(lr.pl_featured(x, 4), model_d4)
#calculate MSEs
mse1 = lr.mean_squared_error(y, estimate_y1)
mse2 = lr.mean_squared_error(y, estimate_y2)
mse3 = lr.mean_squared_error(y, estimate_y3)
mse4 = lr.mean_squared_error(y, estimate_y4)
print("MSE 1D: %f, MSE 2D: %f, MSE 3D: %f, MSE 4D: %f" %
(mse1, mse2, mse3, mse4))
def mse_1d_to_18d(x1, y1, xt, yt):
mse = np.zeros(shape=(18, 1))
for k in range(1, 19):
#calculate w for dimension 1 to 18
model_dk = lr.fit(x1, y1, k)
#calculate estimate value for different dimension
estimate_yt = lr.estimate(lr.pl_featured(xt, k), model_dk)
#calculate MSEs
mse[k - 1] = lr.mean_squared_error(yt, estimate_yt)
return mse
def part1_1_1_a():
#define all variables as global variables
global model_d1, model_d2, model_d3, model_d4
#calculate w for dimension 1 to 4
model_d1 = lr.fit(x, y, 1)
model_d2 = lr.fit(x, y, 2)
model_d3 = lr.fit(x, y, 3)
model_d4 = lr.fit(x, y, 4)
#configuration of plot
plt.xlim(0, 5)
plt.ylim(-4, 8)
plt.xlabel('x')
plt.ylabel('y')
#draw plot
x_axis1 = np.linspace(0, 5, num=1000)
y_axis1 = np.linspace(2.5, 2.5, num=1000)
'''
y_axis2 = 1.5 + 0.4 * x_axis1
y_axis3 = 9 - 7.1 * x_axis1 + 1.5 * x_axis1 ** 2
y_axis4 = -5 + 15.17 * x_axis1 - 8.5 * x_axis1 ** 2 + 1.33 * x_axis1 ** 3
'''
y_axis2 = lr.estimate(lr.pl_featured(x_axis1, 2), model_d2)
y_axis3 = lr.estimate(lr.pl_featured(x_axis1, 3), model_d3)
y_axis4 = lr.estimate(lr.pl_featured(x_axis1, 4), model_d4)
plt.scatter([1, 2, 3, 4], [3, 2, 0, 5])
l1, = plt.plot(x_axis1, y_axis1, color='green', label='dimension 1')
l2, = plt.plot(x_axis1, y_axis2, color='blue', label='dimension 2')
l3, = plt.plot(x_axis1, y_axis3, color='black', label='dimension 3')
l4, = plt.plot(x_axis1, y_axis4, color='red', label='dimension 4')
# Place a legend to the right of this smaller subplot.
plt.legend(handles=[l1, l2, l3, l4],
labels=['k=1', 'k=2', 'k=3', 'k=4'],
loc='best')
plt.show()