The plan in this short note is to briefly consider how we might go about
extending the GaussianProcessRegressor class in the sci-kit learn module
to easy allow us to perform Gaussian process regression while specifying a prior.
First it is worth demonstrating that it is relatively simple to construct an example
of a Gaussian process for which the maximum likelihood value of the kernel
hyperparameter collapses to an uninteresting degerate limit
Kernel with Prior
First step is to
Extending the GaussianProcessRegressor
class GaussianProcessRegress(
sklearn.gaussian_process.GaussianProcessRegressor):
def log_marginal_likelihood(self, theta=None, eval_gradient=None):
if hasattr(self.kernel, 'theta_prior'):
if eval_gradient:
ll, ll_grad = super().log_marginal_likelihood()
lp, lp_grad = prior.logpdf(theta, eval_gradient=True)
return ll + lp, ll_grad + lp_grad
else:
ll = super().log_marginal_likelihood()
lp = prior.logpdf(theta)
return ll + lp
else:
return super().log_marginal_likelihood(theta, eval_gradient)