# Gaussian process regression for large dimensional input space

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 $$\mathbf{x}$$?