I'm fitting a Gaussian process regression model in MATLAB (using the quasi-Newton method) with 10 input parameters, using the Matérn 5/2 and Matérn 5/2 ARD kernels.

I notice that, with increasing number of data points, the training time for the ARD variant grows exponentially while for the non-ARD variant it grows almost linearly.

I understand that there are more parameters to estimate in the ARD kernel, but why exactly is it so much more expensive? Does it hold in general, that GP's with ARD kenerls are more expensive to train?


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