Covariance Function (i.e. Kernel Function)

• used in Gaussian Process Regression (GPR) - Kriging

They encode all assumptions about the form of function that we are modeling. In general, covariance represents some form of distance or similarity. Consider two input points (locations) 𝑥_𝑖 and 𝑥_𝑗 with the corresponding observed values 𝑦_𝑖 and 𝑦_𝑗. If the inputs 𝑥_𝑖 and 𝑥_𝑗 are close to each other, we generally expect that 𝑦_𝑖 and 𝑦_𝑗 will be close as well. This measure of similarity is embedded in the covariance function

Covariance Function - Types

• the most common type is the Gaussian Kernel Function (aka Squared Exponential Covariance Function)
• for others see: Kernel Functions (Similarity Functions)

Resources

• http://evelinag.com/Ariadne/covarianceFunctions.html