The derivation of gradient of the marginal likelihood is given in this pdf, equation 5.9. But the gradient for the most commonly used covariance function, squared exponential covariance, is not explicitly given. (or the second order derivative)

I am implementing the Rprop algorithm in this pdf, section 2 for learning hyper-parameters sigma (signal variance) and h (length). Alas, my implementation is not working well. I have derived the gradients and I suspect I did something wrong.

(Squared exponential covariance function: $k(x,x')=\sigma \exp\left(\frac{||x-x'||^2}{2h^2}\right)$

Can someone point me to a good tutorial / article that explicitly give the expressions for the hyper parameter gradients?

  • $\begingroup$ Can you add some of the necessary context into the question? People may not want to read these pdfs just so they can understand & answer this question. Also, the links may go dead over time. $\endgroup$ Nov 20, 2014 at 16:57
  • $\begingroup$ Okay. I added a reference to the section and equation number. $\endgroup$
    – aaronqli
    Nov 20, 2014 at 17:06

1 Answer 1


Check out my post here which will show you and explain how it is implemented in most libraries.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.