能否提供一个示例？我正在尝试将其用于5D输入。另外，我如何为每个输入绘制与输出的图表？我只有一个输出维度。我的想法是传递一些训练集数据，然后使用测试数据集验证输出。我想传递一个5D（X1 X2 X3 X4 X5）的输入，其中我有1600个数据点。目前我只有X1作为输入
这是代码:
from matplotlib import pyplot as pltfrom sklearn.gaussian_process import GaussianProcessRegressorfrom sklearn.base import BaseEstimatorfrom sklearn.gaussian_process.kernels import RBF, Matern, WhiteKernel, ConstantKernel, RationalQuadratic, ExpSineSquared, DotProduct# define Kernelimport numpy as npkernels = [1.0 * RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0)), 1.0 * Matern(length_scale=1.0, length_scale_bounds=(1e-1, 10.0), nu=1.5), 1.0 * RationalQuadratic(length_scale=1.0, alpha=0.1), 1.0 * ExpSineSquared(length_scale=1.0, periodicity=3.0, length_scale_bounds=(0.1, 10.0), periodicity_bounds=(1.0, 10.0)), ConstantKernel(0.1, (0.01, 10.0)) * (DotProduct(sigma_0=1.0, sigma_0_bounds=(0.0, 10.0)) ** 2), ]# Define inputs and outputsx = np.array([-5.2,-3,-2,-1,1,5], ndmin=2).TX = x.reshape(-1, 1)y =np.array([-2,0,1,2,-1,1])max_x = max(x)min_x = min (x)max_y = max (y)min_y = min(y)for fig_index, kernel in enumerate(kernels): # call GP regression library and fit inputs to output gp = gaussian_process.GaussianProcessRegressor(kernel=kernel) gp.fit(X, y)# parameter = get_params(deep=True)# print(parameter) gp.kernel_ print(gp.kernel_) plt.figure(fig_index, figsize=(10,6)) plt.subplot(2,1,1) x_pred = np.array(np.linspace(-5, 5,50), ndmin=2).T # Mark the observations plt.plot(X, y, 'ro', label='observations') X_test = np.array(np.linspace(max_x+1, min_x-1, 1000),ndmin=2).T y_mean, y_std = gp.predict(X_test, return_std=True) # Draw a mean function and 95% confidence interval plt.plot(X_test, y_mean, 'b-', label='mean function') upper_bound = y_mean +y_std lower_bound = y_mean - y_std plt.fill_between(X_test.ravel(), lower_bound, upper_bound, color = 'k', alpha = 0.2, label='95% confidence interval') # plot posterior y_sample = gp.sample_y(X_test,4) plt.plot(X_test,y_sample,lw=1) plt.scatter(X[:,0],y,c='r',s=50,zorder=10,edgecolor=(0,0,0)) plt.title("Posterior (kernel:%s)\n Log-Likelihood: %3f" % (gp.kernel_, gp.log_marginal_likelihood(gp.kernel_.theta)), fontsize=14) plt.tight_layout() plt.show()回答：
在使用多输入进行GP回归时，除了在各向异性情况下需要在核函数定义中明确提供相关参数外，没有什么特别之处。
这里是一个简单示例，使用与您类似的虚拟5D数据和各向同性的RBF核函数:
from sklearn.gaussian_process import GaussianProcessRegressorfrom sklearn.gaussian_process.kernels import RBFfrom sklearn.datasets import make_regressionimport numpy as np# dummy data:X, y = make_regression(n_samples=20, n_features=5, n_targets=1)X.shape# (20, 5)kernel = RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0))gp = GaussianProcessRegressor(kernel=kernel)gp.fit(X, y)# GaussianProcessRegressor(alpha=1e-10, copy_X_train=True,# kernel=RBF((length_scale=1), n_restarts_optimizer=0,# normalize_y=False, optimizer='fmin_l_bfgs_b',# random_state=None)更新：在各向异性情况下，您应该在核函数中明确定义不同的参数；这里是一个RBF核函数和一个2D变量的示例定义:
kernel = RBF(length_scale=[1.0, 2.0], length_scale_bounds=[(1e-1, 10.0), (1e-2, 1.0)])对于5D情况，相应地进行扩展。
