On Wed, Nov 26, 2008 at 02:55:08PM -0500, Abram Demski wrote:
>
> Russel,
>
> I do not see why some appropriately modified version of that theorem
> couldn't be proven for other settings. As a concrete example let's
> just use Schmidhuber's GTMs. There would be universal GTMs and a
> constant cost for conversion and everything else needed for a version
> of the theorem, wouldn't there be? (I am assuming things, I will look
> up some details this afternoon... I have the book you refer to, I'll
> look at the theorem... but I suppose I should also re-read the paper
> about GTMs before making bold claims...)
>
> --Abram
>
IIRC, Schmidhuber's machines were non-prefix Turing machines. As such
there may or may not be a probability distribution in the first
place. Solomonoff's original proposal using universal Turing machine
didn't work because the probability distribution could not be defined.
If, however, a probility distribution could be defined, then it would
probably end up being equivalent to the S-L universal prior.
Cheers
--
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A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Thu Nov 27 2008 - 05:18:57 PST