A theory of information with special application to search problems

Classical information theory concerns itself with communication through a noisy channel and how much one can infer about the channel input from a knowledge of the channel output. Because the channel is noisy the input and output are only related statistically and the rate of information transmission is a statistical concept with little meaning for the individual symbol used in transmission. Here we develop a more intuitive notion of information that is concerned with asking the right questions--that is, with finding those questions whose answer conveys the most information. We call this confirmatory information. In the first part of the paper we develop the general theory, show how it relates to classical information theory, and how in the special case of search problems it allows us to quantify the efficacy of information transmission regarding individual events. That is, confirmatory information measures how well a search for items having certain observable properties retrieves items having some unobserved property of interest. Thus confirmatory information facilitates a useful analysis of search problems and contrasts with classical information theory, which quantifies the efficiency of information transmission but is indifferent to the nature of the particular information being transmitted. The last part of the paper presents several examples where confirmatory information is used to quantify protein structural properties in a search setting.