Create New Lower Dimension Gaussian Process

[SamChill]

I have fit a Gaussian Process to noisy experimental data y = f(x,y,z). I used SingleTaskGP and it does a great job modeling the experimental results. Then want to perform a Bayesian optimization where I find the candidates that maximize g(x,y) = f(x,y,10) - f(x,y,0). I believe that this new g(x,y) should be able to be analytically determined from the original gaussian process and represented as a custom Model that implements a posterior method that returns a new MultivariateNormal.

Can any one suggest how to make a custom model that computes posterior for the difference between two points on an already fit Gaussian Process? Or is there a better way to achieve my goal? I have been able to do this, at least for the means and I can make a contour plot that looks good, but I am getting confused about how to implement this in a way that optimize_acqf likes as it passes multiple batches at once.

[Balandat]

Hmm just to make sure I understand when you say y = f(x,y,z) - are x,y,z the features here and the outcome is something else, or are you indeed regressing an outcome y on itself?

Assuming the former; In terms of how to implement this - you're on the right track with implementing a custom model. The easiest may be to just use a simple wrapper class that takes the fitted model full_gp operating on x,y,z in its constructor, stores it as an attribute, and then implements the posterior(X) method with a two-dim X such that it calls full_gp.posterior(X_aug10) and full_gp.posterior(X_aug0) (where X_aug* is X with the additional value * appended), from which you can compute the new mean an covariance based on mean an covariance from the two constituent posteriors and return this as a GPyTorchPosterior. Then you should be able to initialize this wrapper and pass it into optimize_acqf.