Conditional graph entropy as an alternating minimization problem

Harangi, Viktor and Niu, Xueyan and Bai, Bo (2023) Conditional graph entropy as an alternating minimization problem. IEEE TRANSACTIONS ON INFORMATION THEORY. ISSN 0018-9448

	Text Conditional_Graph_Entropy__as_an_alternating_min_prob__IEEE_format.pdf - Published Version Restricted to Repository staff only Download (547kB) | Request a copy
Preview	Text 2209.00283v3.pdf Download (614kB) | Preview

Abstract

Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csisz´ar, K¨orner, Lov´asz, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm.

Actions (login required)

Edit Item