Implement new fit algorithms: Laplace & Pathfinder

[wpetry]

Carried over from a discussion on Discourse.

Implement Laplace and Pathfinder fitting methods. Laplace method is available since Stan 2.31.0 and Pathfinder since 2.33.0. I think this would limit implementation in brms to the cmdstanr backend due to the lag of RStan.

Implementation would (I think) closely match the existing variational inference support in brms (e.g., via the $variational()method for CmdStanModel objects). The analogous $laplace() and $pathfinder() methods have a lot of the same arguments, though Pathfinder has some additional tuning options that would need documentation (or reference to the existing cmdstanr docs).

[fusaroli]

Side comment:
A use case we have explored is to use pathfinder to identify initial values, so an easy way to feed pathfinder outcomes into the initial values for a new run of brms based on HMC would be ideal

[wpetry]

@fusaroli Could brms build on the approach in-progress for cmdstanr?
stan-dev/cmdstanr#876
I suspect brmsfit objects would need a method that wraps the cmdstanr implementation. If that intuition is correct, it might be best to open a separate issue given that this functionality would have prerequisite features both here and in cmdstanr.

[bachlaw]

Side comment: A use case we have explored is to use pathfinder to identify initial values, so an easy way to feed pathfinder outcomes into the initial values for a new run of brms based on HMC would be ideal

For Pathfinder I think this is THE use case. Reduce sum has been a godsend, but unless you have a cluster to work with, your 4-8 CPUs are best used on only one chain because having multiple chains go through long individual warmups is such a huge suck of time by comparison. If Pathfinder inits could slice the warmup time to, say, 100-250 iterations per chain, with the initial adaptation being pro forma for most models, it could become efficient to run 3 or 4 chains on a personal machine with an extra thread or two per chain, which would make results more robust, much faster. Would be a huge benefit on an already terrific setup, particularly during exploratory work.

[paul-buerkner]

pathfinder and laplace are now supported with the cmdstanr backend

[fusaroli]

awesome, thanks!