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Nonparametric Density Estimation Using Copula Transform, bayesian sequential partitioning, and Diffusion-Based Kernel Estimator

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2020年第4期32卷 821-826页

作者： Majdara, Aref Nooshabadi, Saeid Michigan Technol Univ Dept Elect & Comp Engn Houghton MI 49931 USA Michigan Technol Univ Dept Comp Sci Houghton MI 49931 USA

Non-parametric density estimation methods are more flexible than parametric methods, due to the fact that they do not assume any specific shape or structure for the data. Most non-parametric methods, like Kernel estimation, require tuning of parameters to achieve good data smoothing, a non-trivial task, even in low dimensions. In higher dimensions, sparsity of data in local neighborhoods becomes a challenge even for non-parametric methods. In this paper, we use the copula transform and two efficient non-parametric methods to develop a new method for improved non-parametric density estimation in multivariate domain. After separation of marginal and joint densities using copula transform, a diffusion-based kernel estimator is employed to estimate the marginals. Next, bayesian sequential partitioning (BSP) is used in the joint density estimation.

关键词： Estimation Kernel Bandwidth Histograms Transforms Bayes methods Diffusion processes Multivariate density estimation non-parametric high-dimensional bayesian sequential partitioning copula transform linear diffusion

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Efficient Density Estimation for High-Dimensional Data

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IEEE ACCESS 2022年 10卷 16592-16608页

作者： Majdara, Aref Nooshabadi, Saeid Michigan Technol Univ Dept Elect & Comp Engn Houghton MI 49931 USA

Multivariate density estimation methods typically work well in low dimensions and their extension to data analytics in high dimensions domain has proven challenging. For density estimation in high-dimensional big data domains, the non-parametric bayesian sequential partitioning (BSP) algorithm provides an efficient way of partitioning the sample space, based on bayesian inference. In this paper, we present a detailed analysis of BSP and provide a computationally efficient copula-transformed data structure and algorithm for use in density estimation for data analytics in high dimensions. Using the copula-transformed data structure, we implement the density estimation for marginals in both BSP and kernel density estimation (KDE) methods. The data structures and algorithm are suitably designed for most efficient rendering into parallel processing paradigms of open multi-processing (OPENMP(R)) and message passing interface (MPI).

关键词： Estimation Bayes methods partitioning algorithms Histograms Kernel Data structures Licenses Multivariate density estimation non-parametric high-dimensional bayesian sequential partitioning copula transform

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Efficient Data Structures for Density Estimation for Large High-Dimensional Data 50

Efficient Data Structures for Density Estimation for Large H...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Majdara, Aref Nooshabadi, Saeid Michigan Technol Univ Dept Elect & Comp Engn Houghton MI 49931 USA

ISBN: (纸本)9781467368537

Density estimation is a fundamental part of statistical analysis and data mining. In high-dimensional domains, parametric methods and the commonly used non-parametric methods like histograms or Kernel estimators fail to perform properly. In this paper, we present computationally efficient data structures for efficient implementation of the bayesian sequential partitioning (BSP), as a framework for density estimation in high-dimensional domain. Simulation results are presented to analyze the performance for large high-dimensional datasets.

关键词： Multiveriate Density Estimation Non-parametric High-dimensional bayesian sequential partitioning Classification

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