Extensions of Bayesian sequential partitioning for multivariate density estimation
Abstract/Contents
- Abstract
- 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 tensor-spline expansion of the log-density condition on the partition learned by BSP. Second, we develop a version of BSP that uses oriented cuts to produce non-rectangular 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.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Kim, Hyunki |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering. |
| Primary advisor | Wong, Wing Hung |
| Thesis advisor | Wong, Wing Hung |
| Thesis advisor | Duchi, John |
| Thesis advisor | Gill, John T III |
| Advisor | Duchi, John |
| Advisor | Gill, John T III |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Hyunki Kim. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Hyunki Kim
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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