--- Pei Wang <[EMAIL PROTECTED]> wrote:
> If I know you are against X, while X is not one of the s_i, but some
> general description of it, how can you use the formula?
If you were compressing the message "on topic X I {agree|disagree}" and you
are predicting bit 2 (after compressing bits 7 through 3 = 01100) of the "a"
or "d", then your knowledge becomes useful.
> If the "knowledge" in a data compressor is all at the level of letter
> string, how can it use the knowledge about the theme of a paper to
> compress it better?
It is only at this level because we don't know how to do it better. Text
compression is an AI-hard problem.
http://cs.fit.edu/~mmahoney/compression/rationale.html
>
> Pei
>
> > > For example, "to predict what will happen in the environment" and "to
> > > predict the next input from the environment as a TM" are two very
> > > different problems, at least to me. For the former, the environment
> > > can be described by a hierarchy of concepts with different
> > > granularity, which for the latter, the environment is always described
> > > at the same level.
> > >
> > > For some people in this list, I can predict their opinions on certain
> > > topics with high accuracy, though I have little idea on what letter
> > > will be the first letter of their next post. If I have to predict
> > > that, I'll have to depend on the the occurrence distribution of
> > > English letters, and my knowledge about their opinions play no role.
> > >
> > > Pei
> >
> > There is no difference. The chain rule says that P(s) = PROD_i
> > P(s_i|s_1..i-1), that any probability distribution over string s can be
> > expressed as a product of conditional predictions of consecutive symbols
> in s.
> > If you know that I am for or against X then you have one bit of
> knowledge. A
> > data compressor knowing this can compress a message from me about X one
> bit
> > smaller than a compressor without this knowledge.
> >
> >
> > -- Matt Mahoney, [EMAIL PROTECTED]
-- Matt Mahoney, [EMAIL PROTECTED]
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