# Understanding the graphical model for a GP for regression, from GPML (Rasmussen and Williams, 2006)

The book Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams (2006) provides a graphical model for GP regression but does not explain it in great detail, so I have a few questions about it:

1. Is $$c$$ the number of context points, hence the $$c$$ subscript for $$y_c, f_c, x_c$$?
2. Does "Gaussian field" refer to the fact that all of the (infinite) function evaluations $$f_i$$ are jointly Gaussian?

3. Does this recreated and simplified graphical model also make sense, or is there something wrong about it that I'm missing?

• Thanks for the answer! So could we label the fully-connected latent variables $f_i$ as "Gaussian process" instead of "Gaussian field" to make the diagram less complicated, or would that no longer be accurate? – Christabella Irwanto Feb 16 '20 at 13:33