whose covariance matrix Σ ∈ R m×m is given by the kernel function applied pairwise over the points {x 1 , x 2 , ..., x m }, Σ i,j := k(x i , x j ). The kernel function k(x, x ) quantifies the similarity of NPMs x and x ; hence, the idea in GPs is that the properties f (x) and f (x ) of similar (dissimilar) NPMs x and x are highly (un)correlated. [ ] GPs effectively model the entire function f (x)in a pointwise manner-by assuming eqn. holds for any arbitrary, finite collection of function values on its domain. The mean of zero in eqn. assumes the measurements are centered.