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- Genre: Academic theses
- Creators: Montgomery, Douglas C.
- Creators: Zhou, Shuang
Description
This dissertation proposes a new set of analytical methods for high dimensional physiological sensors. The methodologies developed in this work were motivated by problems in learning science, but also apply to numerous disciplines where high dimensional signals are present. In the education field, more data is now available from traditional sources and there is an important need for analytical methods to translate this data into improved learning. Affecting Computing which is the study of new techniques that develop systems to recognize and model human emotions is integrating different physiological signals such as electroencephalogram (EEG) and electromyogram (EMG) to detect and model emotions which later can be used to improve these learning systems.
The first contribution proposes an event-crossover (ECO) methodology to analyze performance in learning environments. The methodology is relevant to studies where it is desired to evaluate the relationships between sentinel events in a learning environment and a physiological measurement which is provided in real time.
The second contribution introduces analytical methods to study relationships between multi-dimensional physiological signals and sentinel events in a learning environment. The methodology proposed learns physiological patterns in the form of node activations near time of events using different statistical techniques.
The third contribution addresses the challenge of performance prediction from physiological signals. Features from the sensors which could be computed early in the learning activity were developed for input to a machine learning model. The objective is to predict success or failure of the student in the learning environment early in the activity. EEG was used as the physiological signal to train a pattern recognition algorithm in order to derive meta affective states.
The last contribution introduced a methodology to predict a learner's performance using Bayes Belief Networks (BBNs). Posterior probabilities of latent nodes were used as inputs to a predictive model in real-time as evidence was accumulated in the BBN.
The methodology was applied to data streams from a video game and from a Damage Control Simulator which were used to predict and quantify performance. The proposed methods provide cognitive scientists with new tools to analyze subjects in learning environments.
The first contribution proposes an event-crossover (ECO) methodology to analyze performance in learning environments. The methodology is relevant to studies where it is desired to evaluate the relationships between sentinel events in a learning environment and a physiological measurement which is provided in real time.
The second contribution introduces analytical methods to study relationships between multi-dimensional physiological signals and sentinel events in a learning environment. The methodology proposed learns physiological patterns in the form of node activations near time of events using different statistical techniques.
The third contribution addresses the challenge of performance prediction from physiological signals. Features from the sensors which could be computed early in the learning activity were developed for input to a machine learning model. The objective is to predict success or failure of the student in the learning environment early in the activity. EEG was used as the physiological signal to train a pattern recognition algorithm in order to derive meta affective states.
The last contribution introduced a methodology to predict a learner's performance using Bayes Belief Networks (BBNs). Posterior probabilities of latent nodes were used as inputs to a predictive model in real-time as evidence was accumulated in the BBN.
The methodology was applied to data streams from a video game and from a Damage Control Simulator which were used to predict and quantify performance. The proposed methods provide cognitive scientists with new tools to analyze subjects in learning environments.
ContributorsLujan Moreno, Gustavo A. (Author) / Runger, George C. (Thesis advisor) / Atkinson, Robert K (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Villalobos, Rene (Committee member) / Arizona State University (Publisher)
Created2017
Description
In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects.
Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship.
The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.
Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship.
The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.
ContributorsSeo, Kangwon (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Villalobos, J. Rene (Committee member) / Rigdon, Steven E (Committee member) / Arizona State University (Publisher)
Created2017
Description
In mixture-process variable experiments, it is common that the number of runs is greater than in mixture-only or process-variable experiments. These experiments have to estimate the parameters from the mixture components, process variables, and interactions of both variables. In some of these experiments there are variables that are hard to change or cannot be controlled under normal operating conditions. These situations often prohibit a complete randomization for the experimental runs due to practical and economical considerations. Furthermore, the process variables can be categorized into two types: variables that are controllable and directly affect the response, and variables that are uncontrollable and primarily affect the variability of the response. These uncontrollable variables are called noise factors and assumed controllable in a laboratory environment for the purpose of conducting experiments. The model containing both noise variables and control factors can be used to determine factor settings for the control factor that makes the response "robust" to the variability transmitted from the noise factors. These types of experiments can be analyzed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. The methods for the mixture-process variable designs with noise variables considering a restricted randomization are demonstrated and some mixture-process variable designs that are robust to the coefficients of interaction with noise variables are evaluated using fraction design space plots with the respect to the prediction variance properties. Finally, the G-optimal design that minimizes the maximum prediction variance over the entire design region is created using a genetic algorithm.
ContributorsCho, Tae Yeon (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Shunk, Dan L. (Committee member) / Gel, Esma S (Committee member) / Kulahci, Murat (Committee member) / Arizona State University (Publisher)
Created2010
Description
Public health surveillance is a special case of the general problem where counts (or rates) of events are monitored for changes. Modern data complements event counts with many additional measurements (such as geographic, demographic, and others) that comprise high-dimensional covariates. This leads to an important challenge to detect a change that only occurs within a region, initially unspecified, defined by these covariates. Current methods are typically limited to spatial and/or temporal covariate information and often fail to use all the information available in modern data that can be paramount in unveiling these subtle changes. Additional complexities associated with modern health data that are often not accounted for by traditional methods include: covariates of mixed type, missing values, and high-order interactions among covariates. This work proposes a transform of public health surveillance to supervised learning, so that an appropriate learner can inherently address all the complexities described previously. At the same time, quantitative measures from the learner can be used to define signal criteria to detect changes in rates of events. A Feature Selection (FS) method is used to identify covariates that contribute to a model and to generate a signal. A measure of statistical significance is included to control false alarms. An alternative Percentile method identifies the specific cases that lead to changes using class probability estimates from tree-based ensembles. This second method is intended to be less computationally intensive and significantly simpler to implement. Finally, a third method labeled Rule-Based Feature Value Selection (RBFVS) is proposed for identifying the specific regions in high-dimensional space where the changes are occurring. Results on simulated examples are used to compare the FS method and the Percentile method. Note this work emphasizes the application of the proposed methods on public health surveillance. Nonetheless, these methods can easily be extended to a variety of applications where counts (or rates) of events are monitored for changes. Such problems commonly occur in domains such as manufacturing, economics, environmental systems, engineering, as well as in public health.
ContributorsDavila, Saylisse (Author) / Runger, George C. (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Young, Dennis (Committee member) / Gel, Esma (Committee member) / Arizona State University (Publisher)
Created2010
Description
Yield is a key process performance characteristic in the capital-intensive semiconductor fabrication process. In an industry where machines cost millions of dollars and cycle times are a number of months, predicting and optimizing yield are critical to process improvement, customer satisfaction, and financial success. Semiconductor yield modeling is essential to identifying processing issues, improving quality, and meeting customer demand in the industry. However, the complicated fabrication process, the massive amount of data collected, and the number of models available make yield modeling a complex and challenging task. This work presents modeling strategies to forecast yield using generalized linear models (GLMs) based on defect metrology data. The research is divided into three main parts. First, the data integration and aggregation necessary for model building are described, and GLMs are constructed for yield forecasting. This technique yields results at both the die and the wafer levels, outperforms existing models found in the literature based on prediction errors, and identifies significant factors that can drive process improvement. This method also allows the nested structure of the process to be considered in the model, improving predictive capabilities and violating fewer assumptions. To account for the random sampling typically used in fabrication, the work is extended by using generalized linear mixed models (GLMMs) and a larger dataset to show the differences between batch-specific and population-averaged models in this application and how they compare to GLMs. These results show some additional improvements in forecasting abilities under certain conditions and show the differences between the significant effects identified in the GLM and GLMM models. The effects of link functions and sample size are also examined at the die and wafer levels. The third part of this research describes a methodology for integrating classification and regression trees (CART) with GLMs. This technique uses the terminal nodes identified in the classification tree to add predictors to a GLM. This method enables the model to consider important interaction terms in a simpler way than with the GLM alone, and provides valuable insight into the fabrication process through the combination of the tree structure and the statistical analysis of the GLM.
ContributorsKrueger, Dana Cheree (Author) / Montgomery, Douglas C. (Thesis advisor) / Fowler, John (Committee member) / Pan, Rong (Committee member) / Pfund, Michele (Committee member) / Arizona State University (Publisher)
Created2011
Description
This dissertation covers several topics in machine learning and causal inference. First, the question of “feature selection,” a common byproduct of regularized machine learning methods, is investigated theoretically in the context of treatment effect estimation. This involves a detailed review and extension of frameworks for estimating causal effects and in-depth theoretical study. Next, various computational approaches to estimating causal effects with machine learning methods are compared with these theoretical desiderata in mind. Several improvements to current methods for causal machine learning are identified and compelling angles for further study are pinpointed. Finally, a common method used for “explaining” predictions of machine learning algorithms, SHAP, is evaluated critically through a statistical lens.
ContributorsHerren, Andrew (Author) / Hahn, P Richard (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lopes, Hedibert (Committee member) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Arizona State University (Publisher)
Created2023
Description
This dissertation develops versatile modeling tools to estimate causal effects when conditional unconfoundedness is not immediately satisfied. Chapter 2 provides a brief overview ofcommon techniques in causal inference, with a focus on models relevant to the data explored
in later chapters. The rest of the dissertation focuses on the development of novel “reduced
form” models which are designed to assess the particular challenges of different datasets.
Chapter 3 explores the question of whether or not forecasts of bankruptcy cause bankruptcy.
The question arises from the observation that companies issued going concern opinions were
more likely to go bankrupt in the following year, leading people to speculate that the opinions themselves caused the bankruptcy via a “self-fulfilling prophecy”. A Bayesian machine
learning sensitivity analysis is developed to answer this question. In exchange for additional
flexibility and fewer assumptions, this approach loses point identification of causal effects
and thus a sensitivity analysis is developed to study a wide range of plausible scenarios of
the causal effect of going concern opinions on bankruptcy. Reported in the simulations are
different performance metrics of the model in comparison with other popular methods and a
robust analysis of the sensitivity of the model to mis-specification. Results on empirical data
indicate that forecasts of bankruptcies likely do have a small causal effect.
Chapter 4 studies the effects of vaccination on COVID-19 mortality at the state level in
the United States. The dynamic nature of the pandemic complicates more straightforward
regression adjustments and invalidates many alternative models. The chapter comments on
the limitations of mechanistic approaches as well as traditional statistical methods to epidemiological data. Instead, a state space model is developed that allows the study of the
ever-changing dynamics of the pandemic’s progression. In the first stage, the model decomposes the observed mortality data into component surges, and later uses this information in
a semi-parametric regression model for causal analysis. Results are investigated thoroughly
for empirical justification and stress-tested in simulated settings.
ContributorsPapakostas, Demetrios (Author) / Hahn, Paul (Thesis advisor) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Kao, Ming-Hung (Committee member) / Lan, Shiwei (Committee member) / Arizona State University (Publisher)
Created2023
Description
Tracking disease cases is an essential task in public health; however, tracking the number of cases of a disease may be difficult not every infection can be recorded by public health authorities. Notably, this may happen with whole country measles case reports, even such countries with robust registration systems. Eilertson et al. (2019) propose using a state-space model combined with maximum likelihood methods for estimating measles transmission. A Bayesian approach that uses particle Markov Chain Monte Carlo (pMCMC) is proposed to estimate the parameters of the non-linear state-space model developed in Eilertson et al. (2019) and similar previous studies. This dissertation illustrates the performance of this approach by calculating posterior estimates of the model parameters and predictions of the unobserved states in simulations and case studies. Also, Iteration Filtering (IF2) is used as a support method to verify the Bayesian estimation and to inform the selection of prior distributions. In the second half of the thesis, a birth-death process is proposed to model the unobserved population size of a disease vector. This model studies the effect of a disease vector population size on a second affected population. The second population follows a non-homogenous Poisson process when conditioned on the vector process with a transition rate given by a scaled version of the vector population. The observation model also measures a potential threshold event when the host species population size surpasses a certain level yielding a higher transmission rate. A maximum likelihood procedure is developed for this model, which combines particle filtering with the Minorize-Maximization (MM) algorithm and extends the work of Crawford et al. (2014).
ContributorsMartinez Rivera, Wilmer Osvaldo (Author) / Fricks, John (Thesis advisor) / Reiser, Mark (Committee member) / Zhou, Shuang (Committee member) / Cheng, Dan (Committee member) / Lan, Shiwei (Committee member) / Arizona State University (Publisher)
Created2022
Description
This dissertation centers on Bayesian Additive Regression Trees (BART) and Accelerated BART (XBART) and presents a series of models that tackle extrapolation, classification, and causal inference challenges. To improve extrapolation in tree-based models, I propose a method called local Gaussian Process (GP) that combines Gaussian process regression with trained BART trees. This allows for extrapolation based on the most relevant data points and covariate variables determined by the trees' structure. The local GP technique is extended to the Bayesian causal forest (BCF) models to address the positivity violation issue in causal inference. Additionally, I introduce the LongBet model to estimate time-varying, heterogeneous treatment effects in panel data. Furthermore, I present a Poisson-based model, with a modified likelihood for XBART for the multi-class classification problem.
ContributorsWang, Meijia (Author) / Hahn, Paul (Thesis advisor) / He, Jingyu (Committee member) / Lan, Shiwei (Committee member) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Arizona State University (Publisher)
Created2024
Description
Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
ContributorsMancenido, Michelle V (Author) / Montgomery, Douglas C. (Thesis advisor) / Pan, Rong (Thesis advisor) / Borror, Connie M. (Committee member) / Shunk, Dan L. (Committee member) / Arizona State University (Publisher)
Created2016