Abstract
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on the minimum cross-entropy distribution or apply only to distributions with a bounded-volume support or address only equality constraints. The results of this work hold for general moment inequality constraints for probability distributions with possibly unbounded support, and the technical conditions are explicitly on the underlying generalized moment functions. An analytical characterization of the maxent distribution is also derived using results from the theory of constrained optimization in infinite-dimensional normed linear spaces. Several auxiliary results of independent interest pertaining to certain properties of convex coercive functions are also presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3322-3333 |
| Number of pages | 12 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 51 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2005 |
Keywords
- Coercive functions
- Constrained optimization
- Convex analysis
- Cross-entropy
- Differential entropy
- Maximum entropy methods
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences