Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
Displaying 1 - 6 of 6
Filtering by
- All Subjects: Statistics
Description
This dissertation centers on the development of Bayesian methods for learning differ- ent types of variation in switching nonlinear gene regulatory networks (GRNs). A new nonlinear and dynamic multivariate GRN model is introduced to account for different sources of variability in GRNs. The new model is aimed at more precisely capturing the complexity of GRN interactions through the introduction of time-varying kinetic order parameters, while allowing for variability in multiple model parameters. This model is used as the drift function in the development of several stochastic GRN mod- els based on Langevin dynamics. Six models are introduced which capture intrinsic and extrinsic noise in GRNs, thereby providing a full characterization of a stochastic regulatory system. A Bayesian hierarchical approach is developed for learning the Langevin model which best describes the noise dynamics at each time step. The trajectory of the state, which are the gene expression values, as well as the indicator corresponding to the correct noise model are estimated via sequential Monte Carlo (SMC) with a high degree of accuracy. To address the problem of time-varying regulatory interactions, a Bayesian hierarchical model is introduced for learning variation in switching GRN architectures with unknown measurement noise covariance. The trajectory of the state and the indicator corresponding to the network configuration at each time point are estimated using SMC. This work is extended to a fully Bayesian hierarchical model to account for uncertainty in the process noise covariance associated with each network architecture. An SMC algorithm with local Gibbs sampling is developed to estimate the trajectory of the state and the indicator correspond- ing to the network configuration at each time point with a high degree of accuracy. The results demonstrate the efficacy of Bayesian methods for learning information in switching nonlinear GRNs.
ContributorsVélez-Cruz, Nayely (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Moraffah, Bahman (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Berisha, Visar (Committee member) / Arizona State University (Publisher)
Created2023
Description
Linear-regression estimators have become widely accepted as a reliable statistical tool in predicting outcomes. Because linear regression is a long-established procedure, the properties of linear-regression estimators are well understood and can be trained very quickly. Many estimators exist for modeling linear relationships, each having ideal conditions for optimal performance. The differences stem from the introduction of a bias into the parameter estimation through the use of various regularization strategies. One of the more popular ones is ridge regression which uses ℓ2-penalization of the parameter vector. In this work, the proposed graph regularized linear estimator is pitted against the popular ridge regression when the parameter vector is known to be dense. When additional knowledge that parameters are smooth with respect to a graph is available, it can be used to improve the parameter estimates. To achieve this goal an additional smoothing penalty is introduced into the traditional loss function of ridge regression. The mean squared error(m.s.e) is used as a performance metric and the analysis is presented for fixed design matrices having a unit covariance matrix. The specific problem setup enables us to study the theoretical conditions where the graph regularized estimator out-performs the ridge estimator. The eigenvectors of the laplacian matrix indicating the graph of connections between the various dimensions of the parameter vector form an integral part of the analysis. Experiments have been conducted on simulated data to compare the performance of the two estimators for laplacian matrices of several types of graphs – complete, star, line and 4-regular. The experimental results indicate that the theory can possibly be extended to more general settings taking smoothness, a concept defined in this work, into consideration.
ContributorsSajja, Akarshan (Author) / Dasarathy, Gautam (Thesis advisor) / Berisha, Visar (Committee member) / Yang, Yingzhen (Committee member) / Arizona State University (Publisher)
Created2022
Description
This dissertation explores applications of machine learning methods in service of the design of screening tests, which are ubiquitous in applications from social work, to criminology, to healthcare. In the first part, a novel Bayesian decision theory framework is presented for designing tree-based adaptive tests. On an application to youth delinquency in Honduras, the method produces a 15-item instrument that is almost as accurate as a full-length 150+ item test. The framework includes specific considerations for the context in which the test will be administered, and provides uncertainty quantification around the trade-offs of shortening lengthy tests. In the second part, classification complexity is explored via theoretical and empirical results from statistical learning theory, information theory, and empirical data complexity measures. A simulation study that explicitly controls two key aspects of classification complexity is performed to relate the theoretical and empirical approaches. Throughout, a unified language and notation that formalizes classification complexity is developed; this same notation is used in subsequent chapters to discuss classification complexity in the context of a speech-based screening test. In the final part, the relative merits of task and feature engineering when designing a speech-based cognitive screening test are explored. Through an extensive classification analysis on a clinical speech dataset from patients with normal cognition and Alzheimer’s disease, the speech elicitation task is shown to have a large impact on test accuracy; carefully performed task and feature engineering are required for best results. A new framework for objectively quantifying speech elicitation tasks is introduced, and two methods are proposed for automatically extracting insights into the aspects of the speech elicitation task that are driving classification performance. The dissertation closes with recommendations for how to evaluate the obtained insights and use them to guide future design of speech-based screening tests.
ContributorsKrantsevich, Chelsea (Author) / Hahn, P. Richard (Thesis advisor) / Berisha, Visar (Committee member) / Lopes, Hedibert (Committee member) / Renaut, Rosemary (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2023
Description
Understanding customer preference is crucial for new product planning and marketing decisions. This thesis explores how historical data can be leveraged to understand and predict customer preference. This thesis presents a decision support framework that provides a holistic view on customer preference by following a two-phase procedure. Phase-1 uses cluster analysis to create product profiles based on which customer profiles are derived. Phase-2 then delves deep into each of the customer profiles and investigates causality behind their preference using Bayesian networks. This thesis illustrates the working of the framework using the case of Intel Corporation, world’s largest semiconductor manufacturing company.
ContributorsRam, Sudarshan Venkat (Author) / Kempf, Karl G. (Thesis advisor) / Wu, Teresa (Thesis advisor) / Ju, Feng (Committee member) / Arizona State University (Publisher)
Created2017
Description
Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.
ContributorsJones, Scott, Ph.D (Author) / Cochran, Douglas (Thesis advisor) / Berisha, Visar (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ (Committee member) / Arizona State University (Publisher)
Created2019
Description
Degradation process, as a course of progressive deterioration, commonly exists on many engineering systems. Since most failure mechanisms of these systems can be traced to the underlying degradation process, utilizing degradation data for reliability prediction is much needed. In industries, accelerated degradation tests (ADTs) are widely used to obtain timely reliability information of the system under test. This dissertation develops methodologies for the ADT data modeling and analysis.
In the first part of this dissertation, ADT is introduced along with three major challenges in the ADT data analysis – modeling framework, inference method, and the need of analyzing multi-dimensional processes. To overcome these challenges, in the second part, a hierarchical approach, that leads to a nonlinear mixed-effects regression model, to modeling a univariate degradation process is developed. With this modeling framework, the issues of ignoring uncertainties in both data analysis and lifetime prediction, as presented by an International Standard Organization (ISO) standard, are resolved. In the third part, an approach to modeling a bivariate degradation process is addressed. It is developed using the copula theory that brings the benefits of both model flexibility and inference convenience. This approach is provided with an efficient Bayesian method for reliability evaluation. In the last part, an extension to a multivariate modeling framework is developed. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. The advantages of the proposed modeling framework and the effect of ignoring tail dependence are demonstrated through simulation studies. The applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided.
In summary, this dissertation studies and explores the use of statistical methods in analyzing ADT data. All proposed methodologies are demonstrated by case studies.
In the first part of this dissertation, ADT is introduced along with three major challenges in the ADT data analysis – modeling framework, inference method, and the need of analyzing multi-dimensional processes. To overcome these challenges, in the second part, a hierarchical approach, that leads to a nonlinear mixed-effects regression model, to modeling a univariate degradation process is developed. With this modeling framework, the issues of ignoring uncertainties in both data analysis and lifetime prediction, as presented by an International Standard Organization (ISO) standard, are resolved. In the third part, an approach to modeling a bivariate degradation process is addressed. It is developed using the copula theory that brings the benefits of both model flexibility and inference convenience. This approach is provided with an efficient Bayesian method for reliability evaluation. In the last part, an extension to a multivariate modeling framework is developed. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. The advantages of the proposed modeling framework and the effect of ignoring tail dependence are demonstrated through simulation studies. The applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided.
In summary, this dissertation studies and explores the use of statistical methods in analyzing ADT data. All proposed methodologies are demonstrated by case studies.
ContributorsFANG, GUANQI (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Ju, Feng (Committee member) / Hong, Yili (Committee member) / Arizona State University (Publisher)
Created2020