forward and posterior of SingleTask

[skiyohara]

Dear botorch users and delopers,

I'm a beginner of botorc hand wondering the difference between forward and posterior method of SingleTask.
To my understanding, the forward method output N(0,K), where N is multivariate normal distribution and K is gram matrix, respectively. On the other hand, the posterior method output N(0,K+sigma), where sigma is observatoin noise.

However, the predicted standard deviations (pred1.stddev and pred2.stddev) in my case were exacly equal each other.
Here is my toy code.

model = SingleTask(X_train,Y_train)
mll = ExactMarginalLogLikelihood(model.likelihood, gp)
fit_gpytorch_model(mll)

pred1 = model(X_train)
pred2 = model.posterior(X_train)

Any help would be appreciated.

[saitcakmak]

Hi @skiyohara. Model.forward(...) evaluates the model prior. It is typically used by GPyTorch while computing the model posterior. What you get when you call model(X_train) is model.__call__(X_train), which does a lot more than evaluating model.forward. When the model is in eval mode, GPyTorch computes the posterior on call. We generally do not recommend directly using these methods with BoTorch models.

You can think of Model.posterior as a wrapper around the GPyTorch posterior computations. In addition to computing the posterior, it applies any necessary transforms to both inputs and outputs, wraps the MVN in a Posterior object, and ensures that the output has a consistent shape that is expected by the rest of BoTorch APIs. By default, Model.posterior will not add the observation noise to the predictions. It has an observation_noise argument that you can set to True to include observation noise.

[skiyohara]

Thank you for the kind reply. I fully understood.