Markov process regression
Abstract/Contents
- Abstract
- Regression analysis, the process of estimating the relationship between some dependent and independent variables from empirical data is widely used in many fields including medicine, economics, and machine learning. While many different approaches to regression exist, two important distinctions are whether it is assumed that the relationship has a specific parametric form (e.g., linear) and whether the resultant prediction is deterministic (e.g., when minimizing the sum of squares) or probabilistic. When no specific parametric form is assumed and the prediction is probabilistic, the regression is referred to as nonparametric and Bayesian, respectively. In this dissertation, a broad family of nonparametric Bayesian regression models is introduced, where the prior is assumed to be a Markov process. In comparison to the more common Gaussian process prior, this choice has several advantages such as performance which is not dependent on the form of the likelihood functions and the ability to enforce monotonicity of a relationship a priori. A primary contribution of this dissertation is an algorithm for efficiently updating Markov process priors from experimental data. While this algorithm is based on the forward-backward algorithm for discrete hidden Markov models, extension to the continuous case is not trivial. First, since the transition densities for Markov processes cannot be calculated analytically, simulation methods are used instead. Secondly, existing simulation methods can be extremely inefficient for calculating these updated densities. To circumvent this issue, a new simulation technique is developed that significantly improves the efficiency of these calculations. Lastly, some benefits that Markov process regression has over existing regression methods are illustrated through applied problems. In particular, applications in medicine, consumer science, and manufacturing are presented.
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 | Traverso, Michael G |
|---|---|
| Associated with | Stanford University, Department of Management Science and Engineering. |
| Primary advisor | Howard, Ronald A. (Ronald Arthur), 1934- |
| Thesis advisor | Howard, Ronald A. (Ronald Arthur), 1934- |
| Thesis advisor | Chiu, Samuel S |
| Thesis advisor | Shachter, Ross D |
| Advisor | Chiu, Samuel S |
| Advisor | Shachter, Ross D |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Michael G. Traverso. |
|---|---|
| Note | Submitted to the Department of Management Science and Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Michael Gary Traverso
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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