# Wrong choice of covariance function?

I am applying Gaussian process regression (GPR) model on some data assuming covSEiso (a.k.a. RBF) covariance function. I made sure there are no identical data points (but there are similar data points) and gpml still runs into numerical problems when applying Cholesky decomposition on $K+\sigma_{noise}^2$ I matrix. With other choice of covariance function (e.g. Matern with d parameter 1) things run smoothly. Does this mean the GRP with covSEiso was a wrong model to begin with? I want to decide weather to learn how to deal with the numerical problem (e.g. by removing similar data points which is a hassle IMO) or search for a suitable covariance function.

• Not necessarily. You need to give us a bit more information. Which is you sample size? How many predictors do you have? When you say "similar points", which is the ratio between the minimum and the maximum interpoint sample (I assume you have a small enough sample that you can compute all distances easily)? Most importantly, print the valued of the hyperparameters during optimization – DeltaIV Oct 18 '16 at 6:46

• Thank you for your response. Are you suggesting instead of using inverse of $K+\sigma_n^2 I$ (as GPML computes by Cholesky decomposition) to solve the linear system, I should use $\tilde{K}$, a lower-rank approximation of $K$, and take the least-squares approach? – Seeda Dec 27 '16 at 18:27