Problem with deterministic convergence

[szbalazs98]

We try to run PyVBMC on a 5 dimensional computation neuroscience data and we run into the problem that after re-runs the algorithm converges to different results in case of two parameters which have evident correlation ('gpas_soma' and 'k') as you can see it on the corner plots below. These results are from runs on two different target data. The red and blue data are from two separate runs.

The problem is that pyvbmc detects different segments of the long "banana" shaped high density region even though I re-ran it with the same options, bounds and starting points.

Our goal is to efficiently detect the high density part of the parameter space between the bounds. Do you have any advice on what options we should change to deterministically get the best possible results?

Thank you in advance for your help!

[lacerbi]

Thanks for the report. I'd say this is an undesirable but known failure mode. If you have a curved, narrow ridge between parameters, it can be hard for (Py)VBMC to follow it in its entirety in a single run. Each run is likely to find some region and it will expand there depending on which part of the ridge it first finds (this is stochastic since the search is stochastic).

I cannot think of an easy solution to this right now which is not a new research project.

1. The first true solution would be for PyVBMC to learn to nonlinearly warp the space to follow the ridge. Currently it only learns to linearly transform the space. This is quite involved.
2. The second solution, much easier, would be to combine the results from multiple runs in a smart way (not just averaging them). This is something that can be done with the current information in the variational posterior, but coding it up is another small project in itself. It's been on my to do list for the past five years or so. Maybe I can get an LLM to do it for me soon enough.

Solution 2 would solve your issue if you consider in that you would be required to run PyVBMC multiple times (which is also recommended anyhow). Any single run would not be guaranteed, but if you run multiple of them and combine them in this smart way, you would likely recover a large part of the underlying true posterior.

[szkali]

Thank you very much for the fast response! Do you think we might be able to implement the second solution ourselves? If so, could you perhaps provide some further details on how this smart combination should be computed?

[lacerbi]

Can you folks contact me via email?