Implement the Schrödinger-Föllmer sampler

[AdrienCorenflos]

Presentation of the new sampler

The Schrödinger-Föllmer (https://arxiv.org/abs/2106.10880) is essentially a VI algorithm that obtains samples from a target distribution by defining it as the terminal value of an SDE. It is a bit reminiscent of diffusion models in this respect. The drift in the SDE is expressed as a ratio of two expectations, so that it is typically approximated under samples.

It has since been improved https://arxiv.org/abs/2203.03013 to be able to obtain unbiased estimates of expectations with fairly low bias (note this improvement does not return samples).

How does it compare to other algorithms in blackjax?

• Performance: It is the only "exact" sampler. It does not require ergodicity, and contrary to other VI it can produce exact samples under increasingly computational resources. Also, all samples obtained are independent, so it's amenable to parallelisation.
• Generality: Very general
• Complexity: Fairly easy to implement

Where does it fit in blackjax

Likely VI.

[AdrienCorenflos]

The authors just dropped an improvement on the method

https://arxiv.org/abs/2401.06325

[junpenglao]

I guess you volunteered to implement it :sweat_smile: LOL