def sgd_simple_learning_schedule():
"""SGD use simple_learning_schedule."""
n_epochs = 50
t0, t1 = 5, 50 # learning schedule hyperparameters
def learning_schedule(t):
return t0 / (t + t1)
theta = np.random.randn(2, 1) # random initialization
m = len(x_b)
rnd.seed(42)
for epoch in range(n_epochs):
for i in range(m):
if epoch == 0 and i < 20:
y_predict = x_new_b.dot(theta)
style = "b-" if i > 0 else "r--"
plt.plot(x_new, y_predict, style)
random_index = np.random.randint(m)
xi = x_b[random_index:random_index + 1]
yi = y[random_index:random_index + 1]
gradients = 2 * xi.T.dot(xi.dot(theta) - yi)
eta = learning_schedule(epoch * m + i)
theta = theta - eta * gradients
logger.info('theta :{}'.format(theta))
plt.plot(x, y, "b.")
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.axis([0, 2, 0, 15])
save_img_and_show(name="sgd_plot")
def main():
m = 100
x = 6 * np.random.rand(m, 1) - 3
y = 0.5 * x**2 + x + 2 + np.random.randn(m, 1)
plt.plot(x, y, 'b.')
plt.xlabel('$x_1$', fontsize=18)
plt.ylabel('$y$', rotation=0, fontsize=18)
plt.axis([-1, 3, 0, 10])
save_img_and_show(name='Genearated nonlinear & noisy dataset')
# Use skl
poly_features = PolynomialFeatures(degree=2, include_bias=False)
x_poly = poly_features.fit_transform(x)
logger.info('x[0] {}'.format(x[0]))
logger.info('x_poly[0] {}'.format(x_poly[0]))
lin_reg = LinearRegression()
lin_reg.fit(x_poly, y)
logger.info('lin_reg.intercept_ {}'.format(lin_reg.intercept_))
logger.info('lin_reg.coef_ {}'.format(lin_reg.coef_))
x_new = np.linspace(-3, 3, 100).reshape(100, 1)
x_new_poly = poly_features.transform(x_new)
y_new = lin_reg.predict(x_new_poly)
plt.plot(x, y, 'b.')
plt.plot(x_new, y_new, 'r-', linewidth=2, label="Predictions")
plt.xlabel('$x_1$', fontsize=18)
plt.ylabel('$y$', rotation=0, fontsize=18)
plt.legend(loc="upper left", fontsize=14)
plt.axis([-3, 3, 0, 10])
save_img_and_show(name="PolynomialRegressionModelPredictions")
def polynomial_10degree():
polynomial_regression = Pipeline((
('poly_features', PolynomialFeatures(degree=10, include_bias=False)),
('sgd_reg', LinearRegression()),
))
plot_learning_curves(polynomial_regression, x, y)
plt.axis([0, 80, 0, 3])
save_img_and_show('learning_curves_plot')
def ridge_regression():
"""Ridge Regression."""
plt.figure(figsize=(8, 4))
plt.subplot(121)
plot_model(Ridge, polynomial=False, alphas=(0, 10, 100))
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.subplot(122)
plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1))
save_img_and_show(name="ridge_regression_plot")
def normal_equation_skl():
"""Linear regression model predictions use skl."""
lin_reg = LinearRegression()
lin_reg.fit(x, y)
logger.info('intercept_ {}'.format(lin_reg.intercept_))
logger.info('coef_ {}'.format(lin_reg.coef_))
y_predict = lin_reg.predict(x_new)
logger.info('predict {}'.format(y_predict))
plt.plot(x_new, y_predict, "r-")
plt.plot(x, y, "b.")
plt.axis([0, 2, 0, 15])
save_img_and_show(name='linear regression model predictions skl')
def main():
"""Main."""
logger.info('Lasso Regression')
plt.figure(figsize=(8, 4))
plt.subplot(121)
plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1))
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.subplot(122)
# Show different alpha of lasso regression
plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1)
save_img_and_show(name="lasso_regression_plot")
plt.show()
def normal_equation():
"""normal_equation."""
logger.debug(x)
logger.debug(y)
plt.scatter(x, y)
save_img_and_show(name='randomly_generated_linear_dataset')
theta_best = np.linalg.inv(x_b.T.dot(x_b)).dot(x_b.T).dot(y)
logger.info('\nEquation y = 4 + 3x0 + Gaussionnoise. theta_best {}'.format(
theta_best))
y_predict = x_new_b.dot(theta_best)
logger.info('y_predict {}'.format(y_predict))
plt.plot(x_new, y_predict, "r-")
plt.plot(x, y, "b.")
plt.axis([0, 2, 0, 15])
save_img_and_show(name='linear regression model predictions')
def high_degree_polynomial_regression():
"""High-degree Polynomial Regression."""
for style, width, degree in (("g-", 1, 300), ("b--", 2, 2), ("r-+", 2, 1)):
polybig_features = PolynomialFeatures(degree=degree,
include_bias=False)
std_scaler = StandardScaler()
lin_reg = LinearRegression()
polynomial_regression = Pipeline((
("poly_features", polybig_features),
("std_scaler", std_scaler),
("lin_reg", lin_reg),
))
polynomial_regression.fit(x, y)
y_newbig = polynomial_regression.predict(x_new)
plt.plot(x_new, y_newbig, style, label=str(degree), linewidth=width)
plt.plot(x, y, "b.", linewidth=3)
plt.legend(loc="upper left")
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.axis([-3, 3, 0, 10])
save_img_and_show(name='high_degree_polynomials_plot')
def learning_curves():
lin_reg = LinearRegression()
plot_learning_curves(lin_reg, x, y)
plt.axis([0, 80, 0, 3])
save_img_and_show(name='learning_curves')
