Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones

Abstract

The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimation for a certain exponential family over a cone of this class.

Keywords

• convex cone
• homogeneous cone
• graphical model
• Koszul–Vinberg characteristic function