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- All Subjects: Statistics
- Creators: Zheng, Yi
- Creators: Runger, George C.
- Creators: Enders, Craig K.
- Creators: Zhou, Shuang
- Member of: ASU Electronic Theses and Dissertations
Description
With the increase in computing power and availability of data, there has never been a greater need to understand data and make decisions from it. Traditional statistical techniques may not be adequate to handle the size of today's data or the complexities of the information hidden within the data. Thus knowledge discovery by machine learning techniques is necessary if we want to better understand information from data. In this dissertation, we explore the topics of asymmetric loss and asymmetric data in machine learning and propose new algorithms as solutions to some of the problems in these topics. We also studied variable selection of matched data sets and proposed a solution when there is non-linearity in the matched data. The research is divided into three parts. The first part addresses the problem of asymmetric loss. A proposed asymmetric support vector machine (aSVM) is used to predict specific classes with high accuracy. aSVM was shown to produce higher precision than a regular SVM. The second part addresses asymmetric data sets where variables are only predictive for a subset of the predictor classes. Asymmetric Random Forest (ARF) was proposed to detect these kinds of variables. The third part explores variable selection for matched data sets. Matched Random Forest (MRF) was proposed to find variables that are able to distinguish case and control without the restrictions that exists in linear models. MRF detects variables that are able to distinguish case and control even in the presence of interaction and qualitative variables.
ContributorsKoh, Derek (Author) / Runger, George C. (Thesis advisor) / Wu, Tong (Committee member) / Pan, Rong (Committee member) / Cesta, John (Committee member) / Arizona State University (Publisher)
Created2013
Description
Technological advances have enabled the generation and collection of various data from complex systems, thus, creating ample opportunity to integrate knowledge in many decision making applications. This dissertation introduces holistic learning as the integration of a comprehensive set of relationships that are used towards the learning objective. The holistic view of the problem allows for richer learning from data and, thereby, improves decision making.
The first topic of this dissertation is the prediction of several target attributes using a common set of predictor attributes. In a holistic learning approach, the relationships between target attributes are embedded into the learning algorithm created in this dissertation. Specifically, a novel tree based ensemble that leverages the relationships between target attributes towards constructing a diverse, yet strong, model is proposed. The method is justified through its connection to existing methods and experimental evaluations on synthetic and real data.
The second topic pertains to monitoring complex systems that are modeled as networks. Such systems present a rich set of attributes and relationships for which holistic learning is important. In social networks, for example, in addition to friendship ties, various attributes concerning the users' gender, age, topic of messages, time of messages, etc. are collected. A restricted form of monitoring fails to take the relationships of multiple attributes into account, whereas the holistic view embeds such relationships in the monitoring methods. The focus is on the difficult task to detect a change that might only impact a small subset of the network and only occur in a sub-region of the high-dimensional space of the network attributes. One contribution is a monitoring algorithm based on a network statistical model. Another contribution is a transactional model that transforms the task into an expedient structure for machine learning, along with a generalizable algorithm to monitor the attributed network. A learning step in this algorithm adapts to changes that may only be local to sub-regions (with a broader potential for other learning tasks). Diagnostic tools to interpret the change are provided. This robust, generalizable, holistic monitoring method is elaborated on synthetic and real networks.
The first topic of this dissertation is the prediction of several target attributes using a common set of predictor attributes. In a holistic learning approach, the relationships between target attributes are embedded into the learning algorithm created in this dissertation. Specifically, a novel tree based ensemble that leverages the relationships between target attributes towards constructing a diverse, yet strong, model is proposed. The method is justified through its connection to existing methods and experimental evaluations on synthetic and real data.
The second topic pertains to monitoring complex systems that are modeled as networks. Such systems present a rich set of attributes and relationships for which holistic learning is important. In social networks, for example, in addition to friendship ties, various attributes concerning the users' gender, age, topic of messages, time of messages, etc. are collected. A restricted form of monitoring fails to take the relationships of multiple attributes into account, whereas the holistic view embeds such relationships in the monitoring methods. The focus is on the difficult task to detect a change that might only impact a small subset of the network and only occur in a sub-region of the high-dimensional space of the network attributes. One contribution is a monitoring algorithm based on a network statistical model. Another contribution is a transactional model that transforms the task into an expedient structure for machine learning, along with a generalizable algorithm to monitor the attributed network. A learning step in this algorithm adapts to changes that may only be local to sub-regions (with a broader potential for other learning tasks). Diagnostic tools to interpret the change are provided. This robust, generalizable, holistic monitoring method is elaborated on synthetic and real networks.
ContributorsAzarnoush, Bahareh (Author) / Runger, George C. (Thesis advisor) / Bekki, Jennifer (Thesis advisor) / Pan, Rong (Committee member) / Saghafian, Soroush (Committee member) / Arizona State University (Publisher)
Created2014
Description
Missing data are common in psychology research and can lead to bias and reduced power if not properly handled. Multiple imputation is a state-of-the-art missing data method recommended by methodologists. Multiple imputation methods can generally be divided into two broad categories: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution (e.g., multivariate normal). FCS, on the other hand, imputes variables one at a time, drawing missing values from a series of univariate distributions. In the single-level context, these two approaches have been shown to be equivalent with multivariate normal data. However, less is known about the similarities and differences of these two approaches with multilevel data, and the methodological literature provides no insight into the situations under which the approaches would produce identical results. This document examined five multilevel multiple imputation approaches (three JM methods and two FCS methods) that have been proposed in the literature. An analytic section shows that only two of the methods (one JM method and one FCS method) used imputation models equivalent to a two-level joint population model that contained random intercepts and different associations across levels. The other three methods employed imputation models that differed from the population model primarily in their ability to preserve distinct level-1 and level-2 covariances. I verified the analytic work with computer simulations, and the simulation results also showed that imputation models that failed to preserve level-specific covariances produced biased estimates. The studies also highlighted conditions that exacerbated the amount of bias produced (e.g., bias was greater for conditions with small cluster sizes). The analytic work and simulations lead to a number of practical recommendations for researchers.
ContributorsMistler, Stephen (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona (Committee member) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.
ContributorsBlackwell, Kimberly Carol (Author) / Millsap, Roger E (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2011
Description
Designing studies that use latent growth modeling to investigate change over time calls for optimal approaches for conducting power analysis for a priori determination of required sample size. This investigation (1) studied the impacts of variations in specified parameters, design features, and model misspecification in simulation-based power analyses and (2) compared power estimates across three common power analysis techniques: the Monte Carlo method; the Satorra-Saris method; and the method developed by MacCallum, Browne, and Cai (MBC). Choice of sample size, effect size, and slope variance parameters markedly influenced power estimates; however, level-1 error variance and number of repeated measures (3 vs. 6) when study length was held constant had little impact on resulting power. Under some conditions, having a moderate versus small effect size or using a sample size of 800 versus 200 increased power by approximately .40, and a slope variance of 10 versus 20 increased power by up to .24. Decreasing error variance from 100 to 50, however, increased power by no more than .09 and increasing measurement occasions from 3 to 6 increased power by no more than .04. Misspecification in level-1 error structure had little influence on power, whereas misspecifying the form of the growth model as linear rather than quadratic dramatically reduced power for detecting differences in slopes. Additionally, power estimates based on the Monte Carlo and Satorra-Saris techniques never differed by more than .03, even with small sample sizes, whereas power estimates for the MBC technique appeared quite discrepant from the other two techniques. Results suggest the choice between using the Satorra-Saris or Monte Carlo technique in a priori power analyses for slope differences in latent growth models is a matter of preference, although features such as missing data can only be considered within the Monte Carlo approach. Further, researchers conducting power analyses for slope differences in latent growth models should pay greatest attention to estimating slope difference, slope variance, and sample size. Arguments are also made for examining model-implied covariance matrices based on estimated parameters and graphic depictions of slope variance to help ensure parameter estimates are reasonable in a priori power analysis.
ContributorsVan Vleet, Bethany Lucía (Author) / Thompson, Marilyn S. (Thesis advisor) / Green, Samuel B. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Temporal data are increasingly prevalent and important in analytics. Time series (TS) data are chronological sequences of observations and an important class of temporal data. Fields such as medicine, finance, learning science and multimedia naturally generate TS data. Each series provide a high-dimensional data vector that challenges the learning of the relevant patterns This dissertation proposes TS representations and methods for supervised TS analysis. The approaches combine new representations that handle translations and dilations of patterns with bag-of-features strategies and tree-based ensemble learning. This provides flexibility in handling time-warped patterns in a computationally efficient way. The ensemble learners provide a classification framework that can handle high-dimensional feature spaces, multiple classes and interaction between features. The proposed representations are useful for classification and interpretation of the TS data of varying complexity. The first contribution handles the problem of time warping with a feature-based approach. An interval selection and local feature extraction strategy is proposed to learn a bag-of-features representation. This is distinctly different from common similarity-based time warping. This allows for additional features (such as pattern location) to be easily integrated into the models. The learners have the capability to account for the temporal information through the recursive partitioning method. The second contribution focuses on the comprehensibility of the models. A new representation is integrated with local feature importance measures from tree-based ensembles, to diagnose and interpret time intervals that are important to the model. Multivariate time series (MTS) are especially challenging because the input consists of a collection of TS and both features within TS and interactions between TS can be important to models. Another contribution uses a different representation to produce computationally efficient strategies that learn a symbolic representation for MTS. Relationships between the multiple TS, nominal and missing values are handled with tree-based learners. Applications such as speech recognition, medical diagnosis and gesture recognition are used to illustrate the methods. Experimental results show that the TS representations and methods provide better results than competitive methods on a comprehensive collection of benchmark datasets. Moreover, the proposed approaches naturally provide solutions to similarity analysis, predictive pattern discovery and feature selection.
ContributorsBaydogan, Mustafa Gokce (Author) / Runger, George C. (Thesis advisor) / Atkinson, Robert (Committee member) / Gel, Esma (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2012
Description
Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain.
ContributorsMazza, Gina L (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Functional or dynamic responses are prevalent in experiments in the fields of engineering, medicine, and the sciences, but proposals for optimal designs are still sparse for this type of response. Experiments with dynamic responses result in multiple responses taken over a spectrum variable, so the design matrix for a dynamic response have more complicated structures. In the literature, the optimal design problem for some functional responses has been solved using genetic algorithm (GA) and approximate design methods. The goal of this dissertation is to develop fast computer algorithms for calculating exact D-optimal designs.
First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA.
The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency.
The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature.
First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA.
The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency.
The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature.
ContributorsSaleh, Moein (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Runger, George C. (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2015
Description
Though the likelihood is a useful tool for obtaining estimates of regression parameters, it is not readily available in the fit of hierarchical binary data models. The correlated observations negate the opportunity to have a joint likelihood when fitting hierarchical logistic regression models. Through conditional likelihood, inferences for the regression and covariance parameters as well as the intraclass correlation coefficients are usually obtained. In those cases, I have resorted to use of Laplace approximation and large sample theory approach for point and interval estimates such as Wald-type confidence intervals and profile likelihood confidence intervals. These methods rely on distributional assumptions and large sample theory. However, when dealing with small hierarchical datasets they often result in severe bias or non-convergence. I present a generalized quasi-likelihood approach and a generalized method of moments approach; both do not rely on any distributional assumptions but only moments of response. As an alternative to the typical large sample theory approach, I present bootstrapping hierarchical logistic regression models which provides more accurate interval estimates for small binary hierarchical data. These models substitute computations as an alternative to the traditional Wald-type and profile likelihood confidence intervals. I use a latent variable approach with a new split bootstrap method for estimating intraclass correlation coefficients when analyzing binary data obtained from a three-level hierarchical structure. It is especially useful with small sample size and easily expanded to multilevel. Comparisons are made to existing approaches through both theoretical justification and simulation studies. Further, I demonstrate my findings through an analysis of three numerical examples, one based on cancer in remission data, one related to the China’s antibiotic abuse study, and a third related to teacher effectiveness in schools from a state of southwest US.
ContributorsWang, Bei (Author) / Wilson, Jeffrey R (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Reiser, Mark R. (Committee member) / St Louis, Robert (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2017
Description
Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
ContributorsWang, Zhongsheng (Author) / Stufken, John (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2018