7、径向基函数核
import matplotlib.pyplot as plt
import numpy as np
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
def plot_gpr_samples(gpr_model, n_samples, ax):
x = np.linspace(0, 5, 100)
X = x.reshape(-1, 1)
y_mean, y_std = gpr_model.predict(X, return_std=True)
y_samples = gpr_model.sample_y(X, n_samples)
for idx, single_prior in enumerate(y_samples.T):
ax.plot(
x,
single_prior,
linestyle="--",
alpha=0.7,
label=f"Sampled function #{idx + 1}",
)
ax.plot(x, y_mean, color="black", label="Mean")
ax.fill_between(
x,
y_mean - y_std,
y_mean + y_std,
alpha=0.1,
color="black",
label=r"$\pm$ 1 std. dev.",
)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_ylim([-3, 3])
rng = np.random.RandomState(4)
X_train = rng.uniform(0, 5, 10).reshape(-1, 1)
y_train = np.sin((X_train[:, 0] - 2.5) ** 2)
n_samples = 5
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF
kernel = 1.0 * RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0))
gpr = GaussianProcessRegressor(kernel=kernel, random_state=0)
fig, axs = plt.subplots(nrows=2, sharex=True, sharey=True, figsize=(10, 8))
# 先测图
plot_gpr_samples(gpr, n_samples=n_samples, ax=axs[0])
axs[0].set_title("先验分布样本")
# 后测图
gpr.fit(X_train, y_train)
plot_gpr_samples(gpr, n_samples=n_samples, ax=axs[1])
axs[1].scatter(X_train[:, 0], y_train, color="red", zorder=10, label="Observations")
axs[1].legend(bbox_to_anchor=(1.05, 1.5), loc="upper left")
axs[1].set_title("后验分布样本")
fig.suptitle("径向基函数核", fontsize=18)
plt.tight_layout()
