Lower bound noise in SaasPyroModel (#1586)

Summary:
Pull Request resolved: #1586

X-link: facebook/Ax#1338

Inspecting some models where we get the Cholesky errors, I found that the noise is around 1e-14 - 1e-15, which is very small. Adding a lower bound to the noise seems to let the model fit without errors.

Reviewed By: dme65

Differential Revision: D42177954

fbshipit-source-id: 77c7280ad8f0619f40eacb33f62c5c9fe75a76a8

Author: saitcakmak

botorch/models/fully_bayesian.py

@@ -243,7 +243,7 @@ def sample_mean(self, **tkwargs: Any) -> Tensor:
     def sample_noise(self, **tkwargs: Any) -> Tensor:
         r"""Sample the noise variance."""
         if self.train_Yvar is None:
-            return pyro.sample(
+            return MIN_INFERRED_NOISE_LEVEL + pyro.sample(
                 "noise",
                 pyro.distributions.Gamma(
                     torch.tensor(0.9, **tkwargs),