Integrate SSMProblems & GeneralisedFilters with Turing.jl

[mhauru]

SSMProblems.jl establishes interfaces to define and represent state-space models. By limiting the classes of models that can be represented, SSMProblems.jl provides more specific interface and has the potential to be more computationally efficient.

State-space models are probabilistic models, and major classes of them can be seen as distributions that can be both sampled and scored. Through this lens, we can integrate SSMProblems models through the same interface DynamicPPL.jl currently uses to support "submodels".

to_samplable is implemented in TuringLang/DynamicPPL.jl#696, while to_distribution is tracked at TuringLang/DynamicPPL.jl#802. (Please refer to the comment below for more idea of using these interfaces).

[yebai]

We can likely use to_distribution(m::SSMProblem) to support linear Gaussian state-space models. For more general SSMs, we can look into to_sampleable(m::SSMProblem), which samples the latent states using a sampler in GeneralisedFilters—which can be viewed as a "submodel" but has its inference outsourced to GenerasedFilters instead of relying on MCMC on the tracing data structure VarInfo.