|| Critical Slowing Down Near Topological Transitions in Rate-Distortion Problems
||Shlomi Agmon, Etam Benger, Or Ordentlich, Naftali Tishby, The Hebrew University of Jerusalem, Israel|
||D6-S3-T2: Rate-Distortion Theory I
||Monday, 19 July, 22:40 - 23:00
||Monday, 19 July, 23:00 - 23:20
In rate-distortion (RD) problems one seeks reduced representations of a source that meet a target distortion constraint. Such optimal representations undergo topological transitions at some critical rate values, when their cardinality or dimensionality change. We study the convergence time of the Arimoto-Blahut alternating projection algorithms, used to solve such problems, near those critical points, both for the rate-distortion and information bottleneck settings. We argue that they suffer from critical slowing down -- a diverging number of iterations for convergence -- near the critical points. This phenomenon can have theoretical and practical implications for both machine learning and data compression problems.