Online 1. Extensions of Bayesian sequential partitioning for multivariate density estimation [electronic resource] [2014]
 Kim, Hyunki.
 2014.
 Description
 Book — 1 online resource.
 Summary

Density estimation is a fundamental problem in statistic, which can be used as a building block in statistical methods such as classification. Traditional approaches, such as the kernel method, have yielded accurate results when dealing with a moderate amount of data in a low dimensional space, but may perform poorly in higher dimension. Bayesian sequential partitioning (BSP) was proposed to overcome the drawback of traditional methods by applying scalable algorithms to estimate the probability density in higher dimension. The resulting estimate is a piecewise constant function supported on a partition that is learned from the data. In this work, two extensions/enhancements of BSP are proposed to broaden the area of its application. First, a smoothed version of the estimate is obtained by optimizing over a tensorspline expansion of the logdensity condition on the partition learned by BSP. Second, we develop a version of BSP that uses oriented cuts to produce nonrectangular partitions. By allowing more options to build the partition, our estimate is made invariant to the direction of data point distribution. Our numerical experiments show that the resulting estimate can achieve better approximation to the true density compared to standard BSP.
 Also online at

Special Collections
Special Collections  Status 

University Archives  Request via Aeon (opens in new tab) 
3781 2014 K  Inlibrary use 