Role of prior distribution in single round NPE SBI

[ericlizalde]

Hello there,

I am working on a project using SBI to infer two parameters (angles chi, psi between 0 and 180) from time series, which I specify by an array of numbers. I generate all the data in my simulator before performing the inference. Doing so, I generate this data with a certain distribution for the parameters. Since both are polar angles between two axes, their distribution is not uniform but follows a density of sin(·)/2.
I currently use NPE to infer the posterior distributions in a single round. The SNPE requires the definition of a prior, but Torch does not have a predefined sin(·)/2 distribution. I have been using different ones, thinking maybe it would not have an impact on my posterior distribution, since I am doing a single round. My understanding is that in this case, the prior is only used to remove the posterior samples that fall outside the prior's support.

The basic code I am using is:

prior = Independent(Normal(loc=mean * torch.ones(num_dim), scale=std * torch.ones(num_dim)),
                                   reinterpreted_batch_ndims=1) # or any other distribution

density_estimator_build_fn = posterior_nn(model = 'mdn', embedding_net = embedding_net)
inference = SNPE(prior=prior, density_estimator=density_estimator_build_fn)
inference = inference.append_simulations(angles_train, data_train)
density_estimator = inference.train(
                    show_train_summary=True,
                    retrain_from_scratch = True)

posterior = inference.build_posterior(density_estimator)
samples = posterior.sample((100000,), x=data_obs) 
samples_np = samples.detach().cpu().numpy()  # Convert PyTorch tensor to NumPy array

My question is: how and when does the prior defined in the NPE affect the SBI? Should I try to define the prior to be the same distribution as the distribution that I use to sample my parameters? In that case, how can I do it in Torch for sin(·)/2?

As a matter of example, I include here the comparison between the predicted and true values for the two angles in two cases: when the prior inserted is uniform in [0,180] (first), and when it is a Gaussian with mean = std = 90 (second).


As you can see, there are some differences between the two plots. I am fixing the random seed.

Thank you!

Eric Lizalde.

[michaeldeistler]

Hi there,

for single-round SNPE (ie if you do not run a for-loop as shown here), the prior is almost not used. It is only used to reject posterior samples that are outside of the support of the prior. In your case, the prior is Normal, so it has support on the entire real line, and the prior is completely unused. In your other example, you use a Uniform prior, so it does reject some posterior samples (those outside of [0, 180]).

Aside: You do not have to pass the prior at all (if you do not want to the feature of automatically rejecting posterior samples):

inference = SNPE(density_estimator=density_estimator_build_fn)
...

Hope this helps!
Michael

[ericlizalde]

Ok! Thank you, Michael!

[michaeldeistler]

Sure thing!