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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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That is exactly correct. Under some nice conditions, a noisy signal can be used in place of a non-noisy signal and you'll still get an optimal solution. LQG is a weird but practically important special case that reduces to a simpler case.
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This happens to be discrete. It's a minority tradition in nonlinear distributed stochastic control that starts with Hans Witsenhausen that gets into some of it. All done in discrete, the continuous version is impossibly hard so nobody tries. Still have a pile of papers on it
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