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Yes! I was pretty much subtweeting that via Kalman filters, which are the underlying math for the predictive processing theory, to the extent that it has any, as far as I can tell.
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Hmm unless the search function is broken, the only mention of 'Kalman' in my copy of Surfing Uncertainty is a single footnote where it's mentioned that predictive processing 'has common ground with' Kalman filtering, so it doesn't sound like Kalman filters would be used in PP.
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Not sure what you're asking. Kalman filters are a standard part of control toolkits, and they're "optimal" in the sense of being the optimal LQG solution for linear time invariant systems with gaussian noise. They rest on something called the "certainty equivalence principle"
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Thanks, yeah, I was being vague. Kalman filters are optimal for the thing they are optimal for, and then there’s various broader classes of problems for which analogous things are provably optimal (?), and you’d like a strong result for a very broad class that isn’t done…
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The general nonlinear stochastic is intractable. It's a situation similar to navier-stokes, but not as well known. If you write down the general equations, you can sort of poke at it and get some interesting results, but outside of LQG, there are very few usable results.
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