Conjugate Representations and Characterizing Escort Expectations in Information Geometry

Abstract

Based on the maximum entropy (MaxEnt) principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associated escort expectation is naturally introduced and characterized by the generalized score function which has zero-escort expectation. Furthermore, we show that the escort expectation induces a conformal divergence.

Keywords

• conjugate representations
• information geometry
• escort expectations
• deformed exponential functions
• conformal divergences