Representation Dependence in Probabilistic Inference

TL;DR

This paper investigates the concept of representation dependence in probabilistic inference, showing its fundamental nature and proposing a restricted form of invariance using relative entropy as a compromise.

Contribution

It formalizes representation dependence, proves its inevitability under certain conditions, and introduces a family of inference procedures with restricted invariance based on relative entropy.

Findings

Representation independence implies entailment and conflicts with independence assumptions.

Full representation independence is incompatible with basic default assumptions.

A new class of inference procedures with restricted invariance is constructed using relative entropy.

Abstract

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For example, the principle of maximum entropy has been subjected to much criticism due to its representation dependence. There has, however, been almost no work investigating representation dependence. In this paper, we formalize this notion and show that it is not a problem specific to maximum entropy. In fact, we show that any representation-independent probabilistic inference procedure that ignores irrelevant information is essentially entailment, in a precise sense. Moreover, we show that representation independence is incompatible with even a weak default assumption of independence. We then show that invariance under a restricted class of representation changes can form a reasonable compromise between representation independence and other desiderata, and provide a construction of a family of inference procedures that provides such restricted representation independence, using relative entropy.