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I am working for Gaussian process (GP) regression $y=f(\mathbf{x})+\epsilon$ with $\mathbf{x}\in \mathbb{R}^D$ and $D$ can be as large as few 100. I have attempted with the GPML toolbox and the exact inference method (@infExect) and found out it is working fine till $D=50$. I found KISS-GP which suggests that it is suitable for large scale GP. Yet, in GPML @infGrid performed really bad and I found out the following paragraph in section 4 (experiments):

Furthermore, we focus on the ability for SKI to allow a relaxation of Kronecker and Toeplitz methods to arbitrarily located inputs. Since Toeplitz methods are restricted to 1D inputs and Kronecker methods can only be used for low dimensional (e.g., D < 5) input spaces (Saatchi, 2011), we consider lower dimensional problems.

Does this mean that KISS-GP is suitable for only $D<5$ or so? What are some methods (approximate or exact) which can help to learn $f(\mathbf{x})$ with larger dimensional input $\mathbf{x}$?

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