I am using Gaussian Process classification and I want to do log transform of the hyperparameters so that they are all positive. From this www.lce.hut.fi/research/mm/gpstuff/GPstuffDoc.pdf
document, I understand that the derivatives of the marginal likelihood will change when the hyperparameters are transformed to log scale. To obtain the gradients with respect to log transformed hyperparameters, I have to follow the Appendix E of the above mentioned document. Have I understood it correctly?
If I am wrong kindly explain how do I work with log transformed hyperparameters to obtain marginal likelihood and its gradient with respect to hyperparameters.
And also I would like to know whether I should use log transformed hyperparameters in prediction also or change to normal by taking exponential?
If you are trying to learn original hyper-parameters that e.g. make your new hyper-parameters positive (e.g. through exponential applied to the given original hyper-parameters, where the original can be positive or negative), then the only thing you need to do is compute the new gradient/Hessian/whatever derivatives you want with respect to the original hyper-parameters, e.g. taking into account that you are applying exponential/whatever to the original hyper-parameters before evaluating GP likelihoods/derivatives/ etc. Essentially this comes down to the chain rule. You can find references for how to apply chain rules to things like matrices online.