Generating New Beliefs From Old

TL;DR

This paper extends the random-worlds approach for generating degrees of belief from purely objective information to include existing beliefs, introducing three general techniques based on known methods like cross-entropy that yield consistent results.

Contribution

It proposes three novel techniques to incorporate degrees of belief into the random-worlds method, enhancing its ability to handle subjective information.

Findings

All three techniques produce the same beliefs when applied to the random-worlds method.

The techniques are based on well-known approaches such as cross-entropy.

The methods generalize the previous objective-only framework to include subjective beliefs.

Abstract

In previous work [BGHK92, BGHK93], we have studied the random-worlds approach -- a particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (first-order, statistical, and default) information. But allowing a knowledge base to contain only objective information is sometimes limiting. We occasionally wish to include information about degrees of belief in the knowledge base as well, because there are contexts in which old beliefs represent important information that should influence new beliefs. In this paper, we describe three quite general techniques for extending a method that generates degrees of belief from objective information to one that can make use of degrees of belief as well. All of our techniques are bloused on well-known approaches, such as cross-entropy. We discuss general connections between the techniques and in particular show that, although conceptually and technically quite different, all of the techniques give the same answer when applied to the random-worlds method.