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What should I do when my ‘posterior samples are outside the prior support’ in SNPE?

When working with multi-round NPE (i.e., SNPE), you might have experienced the following warning:

Only x% posterior samples are within the prior support. It may take a long time to
collect the remaining 10000 samples. Consider interrupting (Ctrl-C) and switching to
'sample_with_mcmc=True'.

The reason for this issue is described in more detail here, here, and here. The following fixes are possible:

  • use truncated proposals for SNPE (TSNPE) 

    from sbi.inference import NPE
from sbi.utils import RestrictedPrior, get_density_thresholder

inference = NPE(prior)
proposal = prior
for _ in range(num_rounds):
    theta = proposal.sample((num_sims,))
    x = simulator(theta)
    _ = inference.append_simulations(theta, x).train(force_first_round_loss=True)
    posterior = inference.build_posterior().set_default_x(x_o)

    accept_reject_fn = get_density_thresholder(posterior, quantile=1e-4)
    proposal = RestrictedPrior(prior, accept_reject_fn, sample_with="rejection")

  • sample with MCMC: samples = posterior((num_samples,), x=x_o, sample_with_mcmc=True). This approach will make sampling slower, but samples will not “leak”.

  • resort to single-round NPE and (if necessary) increase your simulation budget.

  • if your prior is either Gaussian (torch.distributions.MultivariateNormal) or Uniform (sbi.utils.BoxUniform), you can avoid leakage by using a mixture density network as density estimator. I.e., set density_estimator='mdn' when creating the SNPE inference object. When running inference, there should be a print statement “Using SNPE-C with non-atomic loss”.

  • use a different algorithm, e.g., Sequential NRE and Sequential NLE. Note, however, that these algorithms can have different issues and potential pitfalls.