Hi all. I’m a new joiner to Pyro and have been playing around with the Normalising Flow example and wanted to experiment with a couple of fairly trivial examples. I want to fit a NF to a multivariate Gaussian and generate simple Bernoulli draws via a logit/sigmoid model of the 1st Gaussian parameter.

I generated the data using the following:

```
import pyro
import pyro.distributions as pyro_dist
import pyro.distributions.transforms as T
from pyro.infer import SVI, Trace_ELBO
import torch
size = 20000
z1 = pyro.sample('z1', pyro_dist.Normal(loc=0., scale=1.), sample_shape=(size,)).flatten()
z2 = pyro.sample('z2', pyro_dist.Normal(loc=2. * z1, scale=1.), sample_shape=(1,)).flatten()
p_true = torch.sigmoid(2 * z1)
x = pyro.sample('x', pyro_dist.Bernoulli(probs=p_true), sample_shape=(1,)).reshape((size, -1)).flatten()
z_vals = torch.stack((z1, z2)).T
```

My aim was to try and pull in the functionality in the NF Pyro demo into a model/guide function framework rather than the approach in the example. My attempt is pasted below:

```
def model_mle(z_vals=None, x_vals=None):
beta_z1 = pyro.param('beta_z1', torch.rand(1))
beta_z2 = pyro.param('beta_z2', torch.rand(1))
with pyro.plate('data', x_vals.shape[0]):
base_dist = pyro_dist.Normal(torch.zeros(2), torch.ones(2))
spline_transform = T.spline_coupling(2, count_bins=16)
flow_dist = pyro.sample('Z', pyro_dist.TransformedDistribution(base_dist, [spline_transform]), obs=z_vals)
x = pyro.sample('x',
pyro_dist.Bernoulli(probs=torch.sigmoid(beta_z1 + beta_z2*flow_dist[:, 0])),
obs=x_vals
)
def guide_mle(z_vals=None, x_vals=None):
pass
lr=0.00005
n_steps=2000
pyro.clear_param_store()
adam_params = {"lr": lr}
adam = pyro.optim.Adam(adam_params)
svi = SVI(model_mle, guide_mle, adam, loss=Trace_ELBO())
for step in range(n_steps):
loss = svi.step(z_vals, x)
if step % 100 == 0:
print('[iter {}] loss: {:.4f}'.format(step, loss))
```

The first issue is that my loss is highly volatile and doesn’t appear to converge:

```
[iter 0] loss: 139756.8848
[iter 100] loss: 128274.8037
[iter 200] loss: 162184.8350
[iter 300] loss: 140769.3340
[iter 400] loss: 129621.6895
[iter 500] loss: 151650.7041
[iter 600] loss: 158514.3320
[iter 700] loss: 134495.2383
[iter 800] loss: 146055.1777
[iter 900] loss: 134883.5430
[iter 1000] loss: 176964.1367
```

Although my parameter estimates appear to be correct (close-ish to 0 and 1):

```
pyro.get_param_store().get_state()['params']
>>>{'beta_z1': tensor([0.0111], requires_grad=True),
'beta_z2': tensor([0.9617], requires_grad=True)}
```

Finally, I would like to draw samlpes from the trained model similar to what is done in the example page. I have tried using the `Predictive`

class but that seems to generate discriminative samples rather than new samples from the NF. How could I do this in Pyro?

To summarise, my general questions are:

- Am I training an NF model correctly?
- How can I draw generative samples from a trained SVI model?

Thanks!