about fantasy model

[LiuYang-1997]

I am a novice, and when I see this term, I don’t understand what it means. Can someone explain me?Thank you very much.

[Balandat]

For look-ahead acquisition strategies, we are interested in reasoning about the possible observations we might make at a point in the domain, and how incorporating these would affect the model in the next iteration. A "fantasy observation" at a point x_f is nothing more than a sample y_f = f(x_f) drawn from the current model posterior at x_f. The "fantasy model" associated with that "fake" observation is the current model conditioned on (x_f, y_f).

[LiuYang-1997]

Thank you very much for solving the problem that has bothered me for several days.

[saitcakmak]

Fantasy (GP) model is the model obtained by conditioning the posterior on fantasy observations at given candidate points. A fantasy observation is an observation that is fantasized / drawn / simulated according to the model (predictive) posterior and likelihood at the given point. For the common Gaussian likelihood, this equivalent to drawing a realization from the posterior and adding the observation noise. They're commonly used in look-ahead type acquisition functions, such as knowledge gradient.

[LiuYang-1997]

Thank you very much for solving the problem that has bothered me for several days.