def plot_lambda_effect():
x_training = np.linspace(0, 1, 40)
y_training = exercise_11.sample_gaussian(exercise_11.f, 0, 0.3, x_training)
# Loop through lambda's.
weights_vector = []
for l in range(-5, 15):
# Zip x and y pairs together, fit a curve.
weights_vector.append(PolCurFit(zip(x_training, y_training), 9, labda=10**-l))
x_test = np.linspace(0, 1, 100)
y_test = exercise_11.sample_gaussian(exercise_11.f, 0, 0.3, x_test)
rmse_training = np.zeros((len(weights_vector)))
rmse_test = np.zeros((len(weights_vector)))
i = 0
weights_vector = weights_vector[::-1]
for weights in weights_vector:
poly_output_100 = [eval_polynomial(weights, x) for x in np.linspace(0, 1, 100)]
poly_output_40 = [eval_polynomial(weights, x) for x in np.linspace(0, 1, 40)]
rmse_training[i] = np.sqrt(np.mean((poly_output_40 - y_training)**2))
rmse_test[i] = np.sqrt(np.mean((poly_output_100 - y_test)**2))
i = i + 1
fig, ax = plt.subplots(1)
ppl.plot(ax, np.arange(-14, 6), rmse_training, linewidth=0.75, label='RMSE on training set')
ppl.plot(ax, np.arange(-14, 6), rmse_test, linewidth=0.75, label='RMSE on test set')
ppl.legend(ax, loc='upper right', ncol=2)
ax.set_xlabel('$log_{10} \lambda$')
ax.set_ylabel('RMSE')
ax.set_title('RMSE for the polynomial approximation of sine function')
fig.savefig('exercise_lambda_rmse_plot40.pdf')
def run_on_data(): x_training = np.linspace(0, 1, 40) y_training = exercise_11.sample_gaussian(exercise_11.f, 0, 0.3, x_training) # Loop through polynomial orders. weights = [] for i in range(0, 10): # Zip x and y pairs together, fit a curve. weights.append(PolCurFit(zip(x_training, y_training), i, labda=10**-6)) plot([weights[0], weights[1], weights[3], weights[9]]) plot_rmse(y_training, weights)
def plot_rmse(y_training, weights_vector):
x_test = np.linspace(0, 1, 100)
y_test = exercise_11.sample_gaussian(exercise_11.f, 0, 0.3, x_test)
rmse_training = np.zeros((len(weights_vector)))
rmse_test = np.zeros((len(weights_vector)))
i = 0
for weights in weights_vector:
poly_output_100 = [eval_polynomial(weights, x) for x in np.linspace(0, 1, 100)]
poly_output_40 = [eval_polynomial(weights, x) for x in np.linspace(0, 1, 40)]
rmse_training[i] = np.sqrt(np.mean((poly_output_40 - y_training)**2))
rmse_test[i] = np.sqrt(np.mean((poly_output_100 - y_test)**2))
i = i + 1
fig, ax = plt.subplots(1)
ppl.plot(ax, np.arange(10), rmse_training, linewidth=0.75, label='RMSE on training set')
ppl.plot(ax, np.arange(10), rmse_test, linewidth=0.75, label='RMSE on test set')
ppl.legend(ax, loc='upper right', ncol=2)
ax.set_xlabel('Polynomial order')
ax.set_ylabel('RMSE')
ax.set_title('RMSE for the polynomial approximation of sine function')
fig.savefig('exercise_rmse_plot40.pdf')
