# preprocess data
scaler = StandardScaler()
scaler.fit(X_train)
X_train = scaler.transform(X_train)
X_test = scaler.transform(X_test)
# fit
beta, beta_var = Lasso(X_train, z_train, lambda_=1e-5, r_var=1)
x_surf = np.linspace(0, terrain.shape[1], terrain.shape[1])
y_surf = np.linspace(0, terrain.shape[0], terrain.shape[0])
X_surf, Y_surf, Z_surf = prep_surface(x_surf,
y_surf,
beta,
deg=3,
scaler=scaler)
fig = plt.figure()
ax = plt.axes(projection="3d")
ax.plot_surface(X_surf, Y_surf, Z_surf, cmap="autumn")
ax.set_title(f"Terrain data lasso approximation,\n deg=3 and " \
+ r"$\lambda=10^{-4}$", fontsize=15)
ax.set_xlabel("x", fontsize=12)
ax.set_ylabel("y", fontsize=12)
ax.set_zlabel("z", fontsize=12)
plt.savefig(f"Figures/terrain_lasso_deg3.png", dpi=300)
plt.show()
plt.imshow((Z_surf - terrain)**2,
X = design_matrix(x, y, n=5)
X_train, X_test, z_train, z_test = train_test_split(X, z, test_size=0.35)
# preprocess data
scaler = StandardScaler()
scaler.fit(X_train)
X_train = scaler.transform(X_train)
X_test = scaler.transform(X_test)
# fit
beta, beta_var = Ridge(X_train, z_train, lambda_=1e-2, r_var=1)
x_surf = np.linspace(0, 1, 100)
y_surf = np.linspace(0, 1, 100)
X_surf, Y_surf, Z_surf = prep_surface(x_surf, y_surf, beta, deg=5)
fig = plt.figure()
ax = plt.axes(projection="3d")
ax.plot_surface(X_surf, Y_surf, Z_surf, cmap="autumn")
ax.set_title(f"Franke Function Ridge approximation,\n deg=5, " \
+ f"N=100 and " + r"$\lambda=10^{-2}$", fontsize=15)
ax.set_xlabel("x", fontsize=12)
ax.set_ylabel("y", fontsize=12)
ax.set_zlabel("z", fontsize=12)
plt.savefig(f"Figures/franke_ridge_deg5_N100.png", dpi=300)
plt.show()
plt.imshow((Z_surf - FrankeFunction(X_surf, Y_surf))**2,
cmap="RdYlGn", origin="lower",
extent=[X_surf.min(), X_surf.max(), Y_surf.min(),
MSE_test[i-1], R2_test[i-1] = MSE_R2(z_hat_test, z_test)
# bootstrap
MSE_boots[i-1], bias_boots[i-1], var_boots[i-1] = bias_variance_tradeoff(X, z, B)
# kfold
MSE_kfold[i-1], std_kfold[i-1] = kfold(k, X, z)
print(f"Completed loops: {i}")
# plot example approximations
if i == 5 or i == 10:
x_surf = np.linspace(0, terrain.shape[1], terrain.shape[1])
y_surf = np.linspace(0, terrain.shape[0], terrain.shape[0])
X_surf, Y_surf, Z_surf = prep_surface(x_surf, y_surf, beta, deg=i,
scaler=scaler_train)
fig = plt.figure()
ax = plt.axes(projection="3d")
ax.plot_surface(X_surf, Y_surf, Z_surf, cmap="autumn")
ax.set_title(f"Terrain OLS approximation, deg={i}", fontsize=15)
ax.set_xlabel("x", fontsize=12)
ax.set_ylabel("y", fontsize=12)
ax.set_zlabel("z", fontsize=12)
plt.savefig(f"Figures/terrain_OLS_deg{i}.png", dpi=300)
plt.show()
plt.imshow((Z_surf - terrain)**2, cmap="RdYlGn",
extent=[X_surf.min(), X_surf.max(), Y_surf.max(),
Y_surf.min()])
plt.title(f"OLS prediction error, deg={i}", fontsize=15)