Re: Optimal Prediction

From: Juergen Schmidhuber <>
Date: Mon, 15 Apr 2002 16:15:32 +0200

Wei Dai wrote:
> BTW, isn't the justification for universal prediction taken in this paper
> kind of opposite to the one you took? The abstract says "The problem,
> however, is that in many cases one does not even have a reasonable guess
> of the true distribution. In order to overcome this problem ..." Your
> papers on the other hand assume that the true distribution can be known
> and proposed that it must be the Speed Prior. (Later you said you believe
> it is the Speed Prior with probability 1.) Is this still your position?

Well, I prefer to recall my more cautious fallback position - let us
write down the assumptions, and derive the consequences.

One does not really have to know the true prior; one just needs an upper
bound on its "power". Choose some prior P, and assume the universe is
sampled from a prior less dominant than P. Then predictions according to
P will be rather accurate.

For example, suppose the process computing the universe is not optimally
efficient for some reason. As long as the resource postulate holds the
true prior cannot dominate the Speed Prior, and S-based predictions
will be fine.

Received on Mon Apr 15 2002 - 07:20:33 PDT

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