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 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? 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] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=88202012-ade734
