François-René Rideau (fare) wrote,
François-René Rideau

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Bayesian about what?

So these halfwits say that rational people ought to be bayesian. Sure. But bayesian about just what? By imposing not the right a priori probability distribution (that will eventually be fixed by experience) but the right descriptional paradigm, the right "meta-context", memetic parasites can have even "bayesian" people believe a lot of nonsense; just propose as "independent" facts on which to be bayesians things that are not so independent after all -- by bombarding readers with systematically biased data to evaluate, you will easily tip their opinions toward the direction of your choice; and they don't even have to choose "right" rather than "wrong" -- they only have to accept your problematics, your choice of data to evaluate. That's where Solomonoff induction comes into play.

One way to describe Solomonoff induction is that it consists in being bayesian not about mere disconnected facts, but about whole theories. Whereas "mere" fact-based bayesian reasoning supposes that its considered facts are atomic and independent from each other, which is all the less true since the data one considers comes repeatedly from the same sources, Solomonoff induction considers coherent partial explanations of the universe, which, when they are conflicting, are indeed independent; and though they are not exactly "atomic", partial theories have a structure of inclusion that is precisely what probability computations are designed to take into account. Moreover, Solomonoff induction gives a non-arbitrary structure to the a priori probability distribution, that is universal in the sense that not only is it compatible with arbitrary explanations (and thus to whatever world we actually are in when we use this induction), but it will asymptotically converge (and rather quickly) toward a correct explanation given enough data, all the while being resiliant to overload with biased data.

Tags: algorithmic complexity, bayesian, en, epistemology, induction, models
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