Add factorial smc

[SamDuffield]

Adds SMC factorializer code.

Adaptive resampling doesn't play nice with factorial so we assume resampling is always applied (i.e. no weights carried through). This could probably be documented better.

[SamDuffield]

Ah actually cuthbert SMC applies resampling at the start of the filter_combine. This might be problematic, will think about it more

[AdrienCorenflos]

I'm not willing to change that one lol. Monte Carlo outputs should come weighted rather than resampled to reduce variance.

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[SamDuffield]

I'm not willing to change that one lol. Monte Carlo outputs should come weighted rather than resampled to reduce variance.

agreed! Will try find a solution at the factorial level

[SamDuffield]

Fixed by adding a resampling step within join when non-constant weights are detected. For this implementation it's recommended to set the particle filter's resampling method to do nothing so I added no_resampling to the cuthbertlib atom to facilitate that.

[SamDuffield]

In order to allow a factorial initialisation with shape (F, N, ...) rather than (N, F, ...) I added an optional particle_axis to the particle filter's init_prepare. Wanted to check if you guys think this is ok? @Sahel13 @AdrienCorenflos

[Sahel13]

In order to allow a factorial initialisation with shape (F, N, ...) rather than (N, F, ...) I added an optional particle_axis to the particle filter's init_prepare. Wanted to check if you guys think this is ok? @Sahel13 @AdrienCorenflos

I am trying to find another way to do it right now XD I don't like this change, that argument is difficult to explain for standard smc. We could add a wrapper for init_prepare specific for factorial SMC, so that all code specific for factorial models stay in that one file. I'll make a pr once i'm done.

[SamDuffield]

I am trying to find another way to do it right now XD I don't like this change, that argument is difficult to explain for standard smc. We could add a wrapper for init_prepare specific for factorial SMC, so that all code specific for factorial models stay in that one file. I'll make a pr once i'm done.

Oooh thanks!! One option I thought about is changing the factorial initialisation to be vmap(init_prepare)(model_inputs). But I think we definitely want to avoid this as it means that the initial model_inputs has to have a factorial axis whilst subsequent model_inputs will not as they only act locally (on a few factors).

[SamDuffield]

I'm wondering if this code can be made to cover the EnKF without too much trouble either, maybe in a later PR though

[SamDuffield]

alright @Sahel13 we good to merge this one? (I'm happy my end)

[Sahel13]

Just one final thing, when init_prepare returns an (F, N) shaped output instead of (F, N, 1), we get a shape error when running the filter. Do we want to support this, or are we fine with always requiring an explicit state dimension axis (i'm fine with this)?

[SamDuffield]

Oh good point! We should match cuthbert.smc there (can’t remember if an explicit state dimension is required there or not).

I’d lean no requiring it though since for SMC we can support ArrayTrees not just Arrays for the particles

[Sahel13]

I’d lean no requiring it though since for SMC we can support ArrayTrees not just Arrays for the particles

Yeah standard SMC didn't have this limitation, so I have fixed it.

I've also modified the pyproject.toml, turns out ruff didn't catch that error with the unused import because we were using select instead of extend-select to modify the linting rules, which meant only the rules we specified in select were being enforced.

[Sahel13]

Actually I'll make a separate PR for that to keep git history clean.