Fritz Obermeyer

cc @eb8680

@eb8680 it looks like `AutoGaussian(pyrocov_model)` runs out of GPU memory in constructing a low-rank matrices `precision = sqrt @ sqrt.T`. One possible solution is to use a sqrt(precision) representation in...

Here is the optimized GFVE schedule for my pyro-cov model. It fits in main memory but runs out of GPU memory. ``` Contraction(ops.null, ops.add, frozenset(), (Contraction(ops.logaddexp, ops.add, frozenset({Variable('rate_loc_scale__BOUND_13', Real)}), (Gaussian(...

@fehiepsi do you recall whether Cholesky was sufficient instead of QR? IIRC there was a PyTorch discussion about cheaply testing for positive definiteness or condition number using [torch.linalg.cholesky_ex()](https://pytorch.org/docs/1.9.1/generated/torch.linalg.cholesky_ex.html#torch.linalg.cholesky_ex).

@eb8680 want to pair code next week on the high-level algorithm for variable elimination, continuing our work from https://github.com/pyro-ppl/funsor/compare/tractable-for-gaussians ?

How about ```py import black class Foo: def __str__(self): ugly = ... return black.format_str(ugly, mode=black.FileMode()) ``` for example ```py >>> import black, funsor, torch >>> funsor.set_backend("torch") >>> from funsor.torch.distributions import...

> ...failing with jit. My guess is that jitting needs to be baked into `funsor.adam.Adam` I think you're right, but let's discuss. That's a little different from Pyro where jit...

> op implementations are opaque to Funsor and are only invoked on ... data I seems more natural to me to extend Python's builtin `operator` library by letting e.g. `ops.add`...

@eb8680 Do I understand correctly that this is blocked by #52 and #50 ?

Hmm, I guess we should instead return a `Variable(name, Real)` from `pyro.sample()`. I believe you could then apply `ops.sqrt()`. I wasn't able to get this working in NumPyro, but you...