comparing:
The statistical definition of a model being linear is that the model must be linear in its parameters.
GPR can be defined by using either the function-space view or the weight-space view to reach the formula for the posterior mean and posterior variance.
If we see the weight-space view, we can clearly see that GPR is indeed a linear model with non linear functions of the inputs. The model is defined as a bayesian linear regression model:
- 𝑦̂ = 𝜙(𝐱)𝑇𝐰
- 𝑦 = 𝑦̂ + 𝑒
where:
- 𝐱 denotes the input vector for an input
- 𝜙(𝑋) denotes some basis function applied on the input space
- 𝐰 is the weight vector
- 𝑦̂ is the regression model
- 𝑒 is the error/noise with Gaussian distribution
However, the non-linearity of inputs doesn’t affect the linearity of the model itself. Kindly refer to the derivation in the weight-space view section of http://www.gaussianprocess.org/gpml/chapters/RW2.pdf for more information