16、核脊与高斯过程回归器的比较
import numpy as np
rng = np.random.RandomState(0)
data = np.linspace(0, 30, num=1_000).reshape(-1, 1)
target = np.sin(data).ravel()
training_sample_indices = rng.choice(np.arange(0, 400), size=40, replace=False)
training_data = data[training_sample_indices]
training_noisy_target = target[training_sample_indices] + 0.5 * rng.randn(
len(training_sample_indices)
)
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
import time
from sklearn.gaussian_process.kernels import ExpSineSquared
from sklearn.kernel_ridge import KernelRidge
kernel_ridge = KernelRidge(kernel=ExpSineSquared())
start_time = time.time()
kernel_ridge.fit(training_data, training_noisy_target)
from sklearn.model_selection import RandomizedSearchCV
from sklearn.utils.fixes import loguniform
param_distributions = {
"alpha": loguniform(1e0, 1e3),
"kernel__length_scale": loguniform(1e-2, 1e2),
"kernel__periodicity": loguniform(1e0, 1e1),
}
kernel_ridge_tuned = RandomizedSearchCV(
kernel_ridge,
param_distributions=param_distributions,
n_iter=500,
random_state=0,
)
start_time = time.time()
kernel_ridge_tuned.fit(training_data, training_noisy_target)
start_time = time.time()
predictions_kr = kernel_ridge_tuned.predict(data)
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import WhiteKernel
kernel = 1.0 * ExpSineSquared(1.0, 5.0, periodicity_bounds=(1e-2, 1e1)) + WhiteKernel(
1e-1
)
gaussian_process = GaussianProcessRegressor(kernel=kernel)
start_time = time.time()
gaussian_process.fit(training_data, training_noisy_target)
start_time = time.time()
mean_predictions_gpr, std_predictions_gpr = gaussian_process.predict(
data,
return_std=True,
)
plt.plot(data, target, label="真实信号", linewidth=2, linestyle="dashed")
plt.scatter(
training_data,
training_noisy_target,
color="m",
label="噪声测量",
)
#绘制核脊的预测
plt.plot(
data,
predictions_kr,
label="核脊",
linewidth=2,
linestyle="dashdot",
)
# 绘制高斯过程回归器的预测图
plt.plot(
data,
mean_predictions_gpr,
label="高斯过程回归器",
linewidth=2,
linestyle="dotted",
)
plt.fill_between(
data.ravel(),
mean_predictions_gpr - std_predictions_gpr,
mean_predictions_gpr + std_predictions_gpr,
color="tab:green",
alpha=0.2,
)
plt.legend(loc="lower right")
plt.xlabel("data")
plt.ylabel("target")
_ = plt.title("核脊与高斯过程回归器的比较")
