[Bug]: `GPyTorchPosterior.distribution` typing for non-MVN likelihood posteriors

[P-Tse]

What happened?

botorch.posteriors.gpytorch.GPyTorchPosterior.distribution can hold distributions that are not MultivariateNormal, including Beta and Bernoulli distributions, depending on the model likelihood.

For instance with a SingleTaskVariationalGP with BetaLikelihood, the posterior with observation noise has a Beta distribution. Is GPyTorchPosterior meant to work with Beta posterior? If the type hint below is correct, it follows that GPyTorchPosterior would be the incorrect class for a Beta posterior distribution?

botorch/botorch/posteriors/gpytorch.py

Line 38 in 5818db2

distribution: MultivariateNormal

Please provide a minimal, reproducible example of the unexpected behavior.

import torch
from botorch.models.approximate_gp import SingleTaskVariationalGP
from gpytorch.distributions import MultivariateNormal
from gpytorch.likelihoods import BetaLikelihood

train_X = torch.rand((20, 10), dtype=torch.double)
train_Y = torch.rand((20, 1), dtype=torch.double)
model = SingleTaskVariationalGP(
    train_X,
    train_Y,
    likelihood=BetaLikelihood(),
)
posterior = model.posterior(train_X, observation_noise=True)
print(f"`posterior` is of type {type(posterior)}")
print(f"Posterior distribution is of type {type(posterior.distribution)}")
print(f"posterior.distribution is an instance of MultivariateNormal: {isinstance(posterior.distribution, MultivariateNormal)}")

Please paste any relevant traceback/logs produced by the example provided.

miniconda3/envs/botorch/lib/python3.12/site-packages/botorch/models/utils/assorted.py:274: InputDataWarning: Data (outcome observations) is not standardized (std = tensor([0.2552], dtype=torch.float64), mean = tensor([0.4533], dtype=torch.float64)).Please consider scaling the input to zero mean and unit variance.
  check_standardization(Y=train_Y, raise_on_fail=raise_on_fail)
`posterior` is of type <class 'botorch.posteriors.gpytorch.GPyTorchPosterior'>
Posterior distribution is of type <class 'pyro.distributions.torch.Beta'>
posterior.distribution is an instance of MultivariateNormal: False

BoTorch Version

0.16.0

Python Version

3.12.12

Operating System

macOS 26.0.1

(Optional) Describe any potential fixes you've considered to the issue outlined above.

Update the type hint

Pull Request

Yes

Code of Conduct

• I agree to follow BoTorch's Code of Conduct

[saitcakmak]

Hi @P-Tse. Despite its name, GPyTorchPosterior does assume that the underlying distribution is an MVN. It may not work correctly with other distributions. For non-MVN torch distributions, I'd recommend using TorchPosterior (or subclassing it if needed) class instead.

[P-Tse]

Thank you for the clarification @saitcakmak.

In my example, if I were to use SingleTaskVariationalGP with non-Gaussian likelihood like Beta, model.posterior(train_X, observation_noise=True) automatically returns a GPyTorchPosterior wrapping the pyro Beta distribution. Are you recommending just getting the Beta distribution from GPyTorchPosterior and wrapping it in TorchPosterior before downstream tasks?

[saitcakmak]

I'm not super familiar with SingleTaskVariationalGP since we don't use it internally. I suspect that the rsample/rsample_with_base_samples methods of GPyTorchPosterior will not be compatible with non-MVN distributions. It might be better to overwrite the posterior implementation of the model to return a TorchPosterior instead.