fix _loc_scale method in AutoMultivariateNormal

[martinjankowiak]

addresses #3232

cc @fritzo

[martinjankowiak]

move "x" so that it's not in the trivial top-left of scale_tril position

[martinjankowiak]

otherwise this test would still pass in master : )

[fritzo]

I assume [0.158655, 0.8413447] == Normal(0, 1).icdf(torch.tensor([-1.0, 1.0]))?

[martinjankowiak]

i can replace with this if you prefer

guide.quantiles(dist.Normal(0, 1).cdf(torch.tensor([-1.0, 1.0])).data.numpy().tolist())

clunky because quantiles wraps in a tensor which raises a user warning if the input is a tensor....

UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).

alternatively can add a comment

[fritzo]

Wouldn't we need a correlated model to test this change? E.g.

def model():
    w = pyro.sample("w", dist.Normal(0.0, 1.0))
    x = pyro.sample("x", dist.Normal(x, 1.0))

[martinjankowiak]

Wouldn't we need a correlated model to test this change? E.g.

def model():
    w = pyro.sample("w", dist.Normal(0.0, 1.0))
    x = pyro.sample("x", dist.Normal(x, 1.0))

i don't think so. we just need to make sure we're computing the correct diagonal element of the full covariance matrix. so as long as we're doing that in a case where that computation is non-trivial (because e.g. it involves off-diagonal elements of scale_tril) we'll be good. as noted in the above comment, it's enough if x is not in the top-left of scale_tril

[martinjankowiak]

@fritzo afaict only quantiles was affected and only the AutoMultivariateNormal autoguide so afaik this PR is complete, pending further comments

[fritzo]

Wouldn't we need a correlated model to test this change?

that computation is non-trivial (because e.g. it involves off-diagonal elements of scale_tril)

My concern is that in the existing test, all those off-diagonal elements happen to be zero, so the old and new formulae happen to agree. Am I missing something?

[martinjankowiak]

the covariance_matrix is not diagonal since we do 100 svi steps (except in the Laplace case where I believe the full hessian is not computed). for example:

[[ 0.96436582  0.01351931 -0.01359293  0.10933437]
 [ 0.01351931  1.28534454  0.07159596  0.01766826]
 [-0.01359293  0.07159596  1.14718362  0.0288711 ]
 [ 0.10933437  0.01766826  0.0288711   0.96723489]]