This way we can define a latent function, u such that u= 𝑓(𝑍) at these IPs. The key idea is that with IPs, the function values at the training points 𝑓(𝑋) are conditionally dependent on the IPs, and thus the joint distribution over f = 𝑓(𝑥) and u= 𝑓(𝑍) is given by: