From ε-entropy to KL-entropy:: Analysis of minimum information complexity density estimation

• 成果类型: Article
• 署名作者: Zhang, Tong
• 署名单位: Yahoo! Inc
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000704
• 发表日期: 2006
• 页码: 2180-2210
• 关键词: posterior distributions; CONVERGENCE; rates

摘要

We consider an extension of E-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In particular, we show that this technique can lead to improvements of some classical results concerning the convergence of minimum description length and Bayesian posterior distributions. Moreover, we are able to derive clean finite-sample convergence bounds that are not obtainable using previous approaches.