Very concentrated posterior

[ali-akhavan89]

Hello,

I have a moderately simple model, where the NN learns the model almost "perfectly" when I feed a lot of data using the NPE method. Then, I guess because the learned posterior becomes very concentrated, I get this warning (which I had seen with SNPE, but it now happens with NPE too):

WARNING:root:Only 0.000% proposal samples are
	accepted. It may take a long time to collect the remaining
	10000 samples. Consider interrupting (Ctrl-C) and switching to
	`build_posterior(..., sample_with='mcmc')`.

Ironically, I won't get this message when I don't provide too many training datasets to the NN (and obviously, the validation payoff is worse). But the problem is that the sampling becomes too slow if I switch to MCMC. So, I was wondering if you have any insights on how to prevent this.

Thank you,
Ali

[satwiksps]

Hello @ali-akhavan89

It looks like your posterior is so concentrated that the default rejection sampling struggles to find valid samples strictly within the prior bounds. Since the network learned "too well," it might be placing the peak probability mass just on the edge or slightly outside your prior (leakage).
You may solve this by disabling the rejection check using the reject_outside_prior argument, which was recently added to sbi (#1705) designed for this situation

# Disable the rejection loop to avoid the 0% acceptance warning
samples = posterior.sample((10000,), reject_outside_prior=False)

This allows the flow to return samples instantly, but they might be slightly outside the prior support. If your simulator is strict (e.g., crashes on negative values), you may need to manually clamp these samples to the bounds.

Hope this helps!

[janfb]

Thanks @satwiksps , that's exactly right!

Another point to check would be the simulator itself, is it really stochastic? If not, then the posterior is in principle a delta function on the true parameter, which will get very tall. That said, as long it is not on the edge of the prior, sampling should work perfectly fine even with rejection outside prior support. Therefore, two other things to check:

• is the simulator stochastic, if not, add a bit of Gaussian observation noise
• check whether the true parameter happens to be on the edge of the prior, or plot the prior distribution together with the posterior samples

[ali-akhavan89]

Thank you both.
Jan, I think you're right. The simulator is stochastic, but the outcome variable is smoothed out, and there's no Gaussian measurement noise applied to it. As a result, I think the NN is perfectly trained, and the posterior becomes like a delta function. 

I think, as you pointed out, the solution is to include some ad-hoc Gaussian noise on the measured variables, or change the parameters of the network to prevent overfitting. For example, if I increase batch_size for training datasets, the validation payoff is not perfect anymore, and I won't get the 0% acceptance warning.

Another practical note: I generated the ground truth data using the proprietary software on Windows. But I'm translating the model using a manually written Python script and training the NN on a Linux cluster. I know that the software on Windows suffers from a small amount of numerical instability. These tiny differences also had an impact on the performance because the model I'm using on Linux has a higher precision than the one that generated the ground truth data. Now that I regenerated the data on Linux using the same true parameters, posterior samples are collected at a much faster pace, even without the Gaussian measurement noise.