高斯过程wrt特征的偏导数

如何解决高斯过程wrt特征的偏导数

给出具有多维特征和标量观测值的高斯过程模型，如何在GPyTorch或GPFlow（或scikit-learn）中计算每个输入的输出wrt的导数？

解决方法

如果我正确理解了您的问题，则以下内容应该会为您提供使用TensorFlow在GPflow中的需求：

import numpy as np
import tensorflow as tf
import gpflow

### Set up toy data & model -- change as appropriate:
X = np.linspace(0,10,5)[:,None]
Y = np.random.randn(5,1)
data = (X,Y)
kernel = gpflow.kernels.SquaredExponential()
model = gpflow.models.GPR(data,kernel)
Xtest = np.linspace(-1,11,7)[:,None]  # where you want to predict

### Compute gradient of prediction with respect to input:
# TensorFlow can only compute gradients with respect to tensor objects,# so let's convert the inputs to a tensor:
Xtest_tensor = tf.convert_to_tensor(Xtest)  

with tf.GradientTape(
        persistent=True  # this allows us to compute different gradients below
) as tape:
    # By default,only Variables are watched. For gradients with respect to tensors,# we need to explicitly watch them:
    tape.watch(Xtest_tensor)

    mean,var = model.predict_f(Xtest_tensor)  # or any other predict function

grad_mean = tape.gradient(mean,Xtest_tensor)
grad_var = tape.gradient(var,Xtest_tensor)