[scikit-learn] Confidence intervals on GaussianProcessRegressor hyperparameters estimates

[Vincent Dubourg]

Hi list,

Did anyone ever considered using the Cramer-Rao lower bound estimate for
the variance-covariance matrix of the GaussianProcess hyperparameters
estimate?

I have seen the gradient of the marginal log likelihood is already
available. How about the hessian matrix?

Looking at the theta values wrt to the one in the fitted kernel themselves,
it looks like some normalization occurs, which is fine, though how do I get
the true gradient back?

Actually, I am more interested in infering the parameters rather than
predicting. I have considered using pymc3 but MCMC is quite time expensive
and I would like to be able to speed this with a reasonable approximation.
George is also an alternative but out of the question since I am running
Windows.

Thank you,
Vincent
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