Gaussian Process Prior (Covariance Function) Sample Clauses

Gaussian Process Prior (Covariance Function). ‌ ( ) ij = ( i⋅ j⋅) ⋅ ∈ × A Gaussian process prior consists of a mean and its covariance function. The mean is often assumed as zero, as empirically we can always zero mean the observed data. The covariance function k x, x is used to model the properties of functions described by the Gaussian process. It builds the covariance matrix K k x , x , where xi is the i-th row of the input matrix X RN Q, of N samples and Q dimen- sions. The covariance function of a GP determines the “shape” of the functions the GP can take. Differentiability of the covariance function at zero for example, determines the “smoothness” of functions generated. The higher the order of differentiability of a covariance function, the smoother the generative function of the GP gets. See some examples of functional shapes in Table 2.1.