CLASSIFICATION ALGORITHMS USING ADAPTIVE PARTITIONING

• 成果类型: Article
• 署名作者: Binev, Peter; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); RWTH Aachen University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1234
• 发表日期: 2014
• 页码: 2141-2163

摘要

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be-viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335-1353; Mach. Learn. 66 (2007) 209-242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter alpha of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness beta of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.