Understanding when to use to_event() in VAE Tutorial

Tutorials
1

I’m going through the Pyro VAE tutorial here (pyro/vae.py at dev · pyro-ppl/pyro · GitHub) but I am struggling to understand how and when to use to_event().

Here’s a bit of code that I am finding confusing:

def model(self, x):
        # register PyTorch module `decoder` with Pyro
        pyro.module("decoder", self.decoder)
        with pyro.plate("data", x.shape[0]):
            # setup hyperparameters for prior p(z)
            z_loc = torch.zeros(x.shape[0], self.z_dim, dtype=x.dtype, device=x.device)
            z_scale = torch.ones(x.shape[0], self.z_dim, dtype=x.dtype, device=x.device)
            # sample from prior (value will be sampled by guide when computing the ELBO)
            z = pyro.sample("latent", dist.Normal(z_loc, z_scale).to_event(1))
            # decode the latent code z
            loc_img = self.decoder.forward(z)
            # score against actual images
            pyro.sample("obs", dist.Bernoulli(loc_img).to_event(1), obs=x.reshape(-1, 784))
            # return the loc so we can visualize it later
            return loc_img

My understanding of to_event() is that it tells pyro that certain dimensions are dependent. But this doesn’t make sense to me here: z = pyro.sample("latent", dist.Normal(z_loc, z_scale).to_event(1)) since in a VAE the latents are independent gaussians. I have read through the documentation on to_event but this is still confusing me. I understand that to_event will reduce the dimension of the batch_shape attribute but I don’t understand why that’s necessary here. Thanks!

2

think of it more so as “these dimensions should be treated as a single event”. this would of course be required if the dimensions were in fact dependent but here we want to treat D-many unit normal random variables as a single MultivariateNormal(zeros(D), eye(D)) distributed random vector

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