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For the RBF Kernel in gaussian_process, the calculation of the gradient seems incorrect?

See original GitHub issue

Description

The RBF kernel corresponds to the form: k(x_i, x_j) = exp(-1/2 ||x_i - x_j||^2 / length_scale^2)

Therefore, the gradient with respect to the parameter length_scale should be: gradient = k(x_i, x_j) * ( ||x_i - x_j||^2 / length_scale^3)

However, the current implementation seems to use the form: gradient = k(x_i, x_j) * ( ||x_i - x_j||^2 / length_scale^2)

Steps/Code to Reproduce

Example:

import numpy as np
from sklearn.gaussian_process.kernels import RBF
np.random.seed(1)
X = np.array([[1,2], [3,4], [5,6]])
sk_kernel = RBF(2.0)
K_grad = sk_kernel(X, eval_gradient=True)[1][:,:,0]

Expected Results

K_grad = 
array([[ 0.        ,  0.36787944,  0.07326256],
       [ 0.36787944,  0.        ,  0.36787944],
       [ 0.07326256,  0.36787944,  0.        ]])

Actual Results

K_grad = 
array([[ 0.        ,  0.73575888,  0.14652511],
       [ 0.73575888,  0.        ,  0.73575888],
       [ 0.14652511,  0.73575888,  0.        ]])

Versions

Darwin-14.5.0-x86_64-i386-64bit Python 3.6.3 (default, Oct 8 2017, 15:07:13) [GCC 4.2.1 Compatible Apple LLVM 7.0.0 (clang-700.0.72)] NumPy 1.13.3 SciPy 0.19.1 Scikit-Learn 0.19.0

Issue Analytics

State:
Created 5 years ago
Reactions:3
Comments:8 (6 by maintainers)

Top GitHub Comments

1reaction

jnothmancommented, May 21, 2018

I agree that’s what it seems to be doing. Could you submit a PR with a test? I’m curious how you found this bug also. We should, if we do not, probably have tests comparing these analytical gradients to numerical estimates.

0reactions

jnothmancommented, Aug 23, 2020

Yes, this is fixed by #18115. Thanks @cmarmo

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