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

Chen, Hongshu

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Chemical Engineering.
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.
Bhavik Bakshi (Advisor)

Recommended Citations

Citations

  • Chen, H. (2007). Sampling-based Bayesian latent variable regression methods with applications in process engineering [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1189650596

    APA Style (7th edition)

  • Chen, Hongshu. Sampling-based Bayesian latent variable regression methods with applications in process engineering. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1189650596.

    MLA Style (8th edition)

  • Chen, Hongshu. "Sampling-based Bayesian latent variable regression methods with applications in process engineering." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1189650596

    Chicago Manual of Style (17th edition)