Minimum Cross-Entropy Reasoning: A Statistical Justification

Abstract

Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more specific degrees of belief. A statistical model for this process then is shown to vindicate the cross-entropy minimization principle as a rule for probabilistic default-inference. 1 Introduction A knowledge based system incorporating reasoning with uncertain information gives rise to quantitative statements of two different kinds: statements expressing statistical information and statements of degrees of belief. "10% of applicants seeking employment at company X who are invited to an interview will get a job there" is a statistical statement. "The likelihood that I will be invited for an interview if I apply for a job at company X is about 0.6" expresses a degree of belief. In this paper, both of these kinds of statements are regarded as probabilistic, i...