Informationmost

Informationmost is a term used in information theory and data analysis to describe a notion of maximal information content associated with a potential observation or feature. While not a standard term in mainstream theory, it is employed in discussions of surprisal and active learning to denote the element that would be most informative to observe under a given model or distribution.

Formal definition often frames informationmost in terms of self-information. For a discrete random variable X with probability mass function p(x), the informationmost value is the outcome x* = argmax_x [-log p(x)]. In words, it is the most surprising or least probable outcome under the current distribution. In continuous settings, the analogous quantity uses differential self-information, -log f(x), with f being the probability density function. The informationmost thus identifies observations with the greatest potential to update beliefs or reduce uncertainty.

Interpretation and use are context-dependent. In Bayesian updating, observing an outcome with high self-information has the largest potential to change the posterior distribution. In active learning or experimental design, selecting data points or experiments that maximize informationmost can lead to faster learning or more efficient information gathering.

Limitations include sensitivity to the chosen model and distribution; focusing solely on the rarest outcomes can overemphasize noise or outliers. Practical use typically requires integrating informationmost with other criteria, such as cost, robustness, and prior knowledge, to avoid misleading conclusions.

See also: surprisal, entropy, information gain, Bayesian updating, active learning.