title: Computational Aspects of Optional Pólya Tree.
abstract: Optional Pólya tree (OPT) is a flexible nonparametric Bayesian prior for density estimation. Despite its merits, the computation for OPT inference is challenging. In this paper we present time complexity analysis for OPT inference and propose two algorithmic improvements. The first improvement, named limited-lookahead optional Pólya tree (LL-OPT), aims at accelerating the computation for OPT inference. The second improvement modifies the output of OPT or LL-OPT and produces a continuous piecewise linear density estimate. We demonstrate the performance of these two improvements using simulated and real date examples.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109.
authors.forename: Hui
authors.initials: H
authors.lastname: Jiang
authors.affiliation: Department of Electrical Engineering, Stanford University, Stanford, CA 94305.
authors.forename: John Chong
authors.initials: JC
authors.lastname: Mu
authors.affiliation: Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305.
authors.forename: Kun
authors.initials: K
authors.lastname: Yang
authors.affiliation: Department of Statistics, University of Virginia, Charlottesville, VA 22904.
authors.forename: Chao
authors.initials: C
authors.lastname: Du
authors.affiliation: Twitter Inc., San Francisco, CA 94103.
authors.forename: Luo
authors.initials: L
authors.lastname: Lu
authors.affiliation: Department of Statistics and Health Research and Policy, Stanford University, Stanford, CA 94305.
authors.forename: Wing Hung
authors.initials: WH
authors.lastname: Wong
keywords: Bayesian nonparametrics; density estimation; recursive partition; smoothing; time complexity