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API for filtered posteriors #110

@simsurace

Description

@simsurace

Since everything in TemporalGPs.jl is build around SSMs, it should be easy to obtain filtered posteriors of various forms, e.g. p(f_t|Y_0,...,Y_t) or p(f_t|Y_0,...,Y_{t-1}) for all t in some range. It seems that e.g. the latter can be done by using some internals like so:

function one_step_ahead_predictions(f, x, y)
    fx = f(x, obs_noise + 1e-6)
    lgssm = build_lgssm(fx)
    F = vcat(x0(lgssm), _filter(lgssm, y)[1:end-1])
    E = emissions(lgssm)
    return predict.(F, E)
end

but

  • not having a complete understanding of the internals, I'm not sure this is correct
  • It would be nice to expose this (or the correct version) as a public API

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