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Sampling-based Bayesian latent variable regression methods with applications in process engineering.

机译:基于采样的贝叶斯潜在变量回归方法及其在过程工程中的应用。

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摘要

Latent variable methods, such as Principal Component Analysis and Partial Least Squares Regression, can handle collinearity among variables by projecting the original data into a lower dimensional space. They are widely applied to build empirical models of chemical and biological processes. With the development of modern experimental and analytical technology, data sets from those processes are getting bigger and more heterogeneous. The increasing complexity of data sets causes traditional latent variables methods to often fail to provide satisfactory modeling results. Meanwhile, prior information about processes and data usually exist in different sources, such as expert knowledge, historical data etc. However, traditional latent variable methods are ill-suited to incorporate such information. Bayesian latent variable methods, such as Bayesian Latent Variable Regression (BLVR) and Bayesian Principal Component Analysis (BPCA) can combine prior information and data via a rigorous probabilistic framework. Since they make use of more information, they can provide models with better quality. However, BPCA and BLVR are optimization-based, which restricts them from modeling high dimensional data sets or providing error bars. They also make restrictive assumptions to make them suitable for the optimization routines. Because of those pitfalls, they have very limited applications in practice.; This dissertation addresses the challenges of making Bayesian latent variable methods practical by developing novel algorithms and a toolbox of sampling-based methods, including a sampling-based BLVR (BLVR-S). BLVR-S is computationally efficient and is able to model high dimensional data sets. It can also readily provide confidence intervals for estimates. An iterative modeling procedure is proposed to deal with hybrid data sets with both continuous and discrete variables. An extended version of BLVR-S is developed to address lack of information about measurement noise in modeling. A generalized BLVR-S is developed to relax the restrictive assumptions of prior distributions. Those methods tackle some practical challenges in Bayesian modeling. The advantages of those Bayesian latent variable regression methods are illustrated in various case studies. Some practical aspects of applying Bayesian latent variable methods are also explored. Through those efforts, the Bayesian latent variable methods are expected to have more practical applications in building empirical models in process engineering.
机译:潜在变量方法(例如主成分分析和偏最小二乘回归)可以通过将原始数据投影到较低维度的空间中来处理变量之间的共线性。它们被广泛地用于建立化学和生物过程的经验模型。随着现代实验和分析技术的发展,来自这些过程的数据集变得越来越大,种类也越来越多。数据集日益增加的复杂性导致传统的潜在变量方法常常无法提供令人满意的建模结果。同时,有关过程和数据的先验信息通常存在于不同的来源,例如专家知识,历史数据等。但是,传统的潜变量方法不适用于合并此类信息。贝叶斯潜变量方法,例如贝叶斯潜变量回归(BLVR)和贝叶斯主成分分析(BPCA),可以通过严格的概率框架将先验信息和数据结合起来。由于他们利用了更多信息,因此可以提供质量更高的模型。但是,BPCA和BLVR基于优化,这限制了它们对高维数据集建模或提供误差线的限制。它们还做出限制性假设,以使其适合优化例程。由于这些缺陷,它们在实践中的应用非常有限。本文通过开发新颖的算法和基于采样的方法工具箱,包括基于采样的BLVR(BLVR-S),解决了使贝叶斯潜变量方法实用化的挑战。 BLVR-S计算效率高,并且能够对高维数据集建模。它还可以轻松提供估计的置信区间。提出了一种迭代建模程序来处理具有连续变量和离散变量的混合数据集。开发了BLVR-S的扩展版本,以解决建模中缺少有关测量噪声的信息的问题。开发了通用的BLVR-S来放宽先前分布的限制性假设。这些方法解决了贝叶斯建模中的一些实际挑战。这些贝叶斯潜变量回归方法的优点在各种案例研究中得到了说明。还探讨了应用贝叶斯潜变量方法的一些实际方面。通过这些努力,贝叶斯潜变量方法有望在建立过程工程的经验模型中有更多的实际应用。

著录项

  • 作者

    Chen, Hongshu.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Engineering Chemical.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 197 p.
  • 总页数 197
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 化工过程(物理过程及物理化学过程);
  • 关键词

  • 入库时间 2022-08-17 11:39:52

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