Hello. I am trying to implement this paper HPF- Gopalan et. al. in Pyro. So far i have a model that works reasonably well with an automatic guide. I am trying to write a custom guide where all my latent variables have a Gamma variational distribution. My model and guide look something like this .

```
@poutine.scale(scale = 1e-4)
def model(data, args):
n_users, n_items = data.shape
a_prime, b_prime, a, c_prime, d_prime, c, K = args
user_plate = pyro.plate("user_plate", n_users)
item_plate = pyro.plate("item_plate", n_items)
comp_plate = pyro.plate("comp_plate", K)
data_plate = pyro.plate("data_plate", size = ndata, subsample_size=sub_size, dim = -2)
with user_plate:
ξ_u = pyro.sample("ξ_u", dist.Gamma(a_prime, a_prime/b_prime))
with item_plate:
η_i = pyro.sample("η_i", dist.Gamma(c_prime, c_prime/d_prime))
with comp_plate:
θ_uk = pyro.sample("θ_uk", dist.Gamma(a, ξ_u).to_event(1))
β_ik = pyro.sample("β_ik", dist.Gamma(c, η_i).to_event(1))
with data_plate as ind:
λ = torch.mm(θ_uk.T, β_ik)
pyro.sample("y", dist.Poisson(λ[ind]).to_event(1), obs = data[ind])
@poutine.scale(scale = 1e-4)
def custom_guide(data, args):
n_users, n_items = data.shape
a_prime, b_prime, a, c_prime, d_prime, c, K = args
Kint = int(K.item())
user_plate = pyro.plate("user_plate", n_users, dim = -1, use_cuda=True)
item_plate = pyro.plate("item_plate", n_items, dim = -1, use_cuda = True)
comp_plate = pyro.plate("comp_plate", K, dim = -2, use_cuda = True)
β_rates, β_shapes = 0.1*torch.ones((Kint, n_items)).to("cuda"), 0.1*torch.ones((Kint, n_items)).to("cuda")
θ_rates, θ_shapes = 0.1*torch.ones((Kint, n_users)).to("cuda"), 0.1*torch.ones((Kint, n_users)).to("cuda")
β_dist = dist.Gamma(β_rates, β_shapes).to_event(1)
θ_dist = dist.Gamma(θ_rates, θ_shapes).to_event(1)
with item_plate:
η_i = pyro.sample("η_i", dist.Gamma(a_prime, a_prime/b_prime))
with user_plate:
ξ_u = pyro.sample("ξ_u", dist.Gamma(c_prime, c_prime/d_prime))
β_ik = pyro.sample("β_ik", β_dist)
θ_uk = pyro.sample("θ_uk", θ_dist)
```

If i replace my custom guide with an automatic generated guide such as `AutoDiagonalNormal`

. It works fine. Using my custom guide. I printed out the `trace.format_shapes`

for both the model and guide.

guide trace

```
Trace Shapes:
Param Sites:
Sample Sites:
user_plate dist |
value 999 |
log_prob |
item_plate dist |
value 2000 |
log_prob |
comp_plate dist |
value 40 |
log_prob |
η_i dist 2000 |
value 2000 |
log_prob 2000 |
ξ_u dist 999 |
value 999 |
log_prob 999 |
β_ik dist 40 | 2000
value 40 | 2000
log_prob 40 |
θ_uk dist 40 | 999
value 40 | 999
log_prob 40 |
```

model trace

```
Trace Shapes:
Param Sites:
Sample Sites:
user_plate dist |
value 999 |
log_prob |
item_plate dist |
value 2000 |
log_prob |
comp_plate dist |
value 40 |
log_prob |
data_plate dist |
value 100 |
log_prob |
ξ_u dist 999 |
value 999 |
log_prob 999 |
η_i dist 2000 |
value 2000 |
log_prob 2000 |
θ_uk dist 40 | 999
value 40 | 999
log_prob 40 |
β_ik dist 40 | 2000
value 40 | 2000
log_prob 40 |
y dist 100 100 | 2000
value 100 | 2000
log_prob 100 100 |
```

Even though they seem to agree i still get an error.

```
ValueError: at site "β_ik", invalid log_prob shape
Expected [], actual [40]
```

Which is kind of confusing. It would be really great if i could get some input on this.