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- All Subjects: Statistics
- Creators: Runger, George C.
- Creators: Wilson, Jeffrey
- Creators: Zhou, Shuang
- Member of: ASU Electronic Theses and Dissertations
Description
Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment on depression. Subjects are scheduled with doctors on a regular basis and asked questions about recent emotional situations. Patients who are experiencing severe depression are more likely to miss an appointment and leave the data missing for that particular visit. Data that are not missing at random may produce bias in results if the missing mechanism is not taken into account. In other words, the missing mechanism is related to the unobserved responses. Data are said to be non-ignorable missing if the probabilities of missingness depend on quantities that might not be included in the model. Classical pattern-mixture models for non-ignorable missing values are widely used for longitudinal data analysis because they do not require explicit specification of the missing mechanism, with the data stratified according to a variety of missing patterns and a model specified for each stratum. However, this usually results in under-identifiability, because of the need to estimate many stratum-specific parameters even though the eventual interest is usually on the marginal parameters. Pattern mixture models have the drawback that a large sample is usually required. In this thesis, two studies are presented. The first study is motivated by an open problem from pattern mixture models. Simulation studies from this part show that information in the missing data indicators can be well summarized by a simple continuous latent structure, indicating that a large number of missing data patterns may be accounted by a simple latent factor. Simulation findings that are obtained in the first study lead to a novel model, a continuous latent factor model (CLFM). The second study develops CLFM which is utilized for modeling the joint distribution of missing values and longitudinal outcomes. The proposed CLFM model is feasible even for small sample size applications. The detailed estimation theory, including estimating techniques from both frequentist and Bayesian perspectives is presented. Model performance and evaluation are studied through designed simulations and three applications. Simulation and application settings change from correctly-specified missing data mechanism to mis-specified mechanism and include different sample sizes from longitudinal studies. Among three applications, an AIDS study includes non-ignorable missing values; the Peabody Picture Vocabulary Test data have no indication on missing data mechanism and it will be applied to a sensitivity analysis; the Growth of Language and Early Literacy Skills in Preschoolers with Developmental Speech and Language Impairment study, however, has full complete data and will be used to conduct a robust analysis. The CLFM model is shown to provide more precise estimators, specifically on intercept and slope related parameters, compared with Roy's latent class model and the classic linear mixed model. This advantage will be more obvious when a small sample size is the case, where Roy's model experiences challenges on estimation convergence. The proposed CLFM model is also robust when missing data are ignorable as demonstrated through a study on Growth of Language and Early Literacy Skills in Preschoolers.
ContributorsZhang, Jun (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Thesis advisor) / Kao, Ming-Hung (Committee member) / Wilson, Jeffrey (Committee member) / St Louis, Robert D. (Committee member) / Arizona State University (Publisher)
Created2013
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
It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set.
ContributorsMilovanovic, Jelena (Author) / Young, Dennis (Thesis advisor) / Reiser, Mark R. (Thesis advisor) / Wilson, Jeffrey (Committee member) / Eubank, Randall (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2011
Description
Today's competitive markets force companies to constantly engage in the complex task of managing their demand. In make-to-order manufacturing or service systems, the demand of a product is shaped by price and lead times, where high price and lead time quotes ensure profitability for supplier, but discourage the customers from placing orders. Low price and lead times, on the other hand, generally result in high demand, but do not necessarily ensure profitability. The price and lead time quotation problem considers the trade-off between offering high and low prices and lead times. The recent practices in make-to- order manufacturing companies reveal the importance of dynamic quotation strategies, under which the prices and lead time quotes flexibly change depending on the status of the system. In this dissertation, the objective is to model a make-to-order manufacturing system and explore various aspects of dynamic quotation strategies such as the behavior of optimal price and lead time decisions, the impact of customer preferences on optimal decisions, the benefits of employing dynamic quotation in comparison to simpler quotation strategies, and the benefits of coordinating price and lead time decisions. I first consider a manufacturer that receives demand from spot purchasers (who are quoted dynamic price and lead times), as well as from contract customers who have agree- ments with the manufacturer with fixed price and lead time terms. I analyze how customer preferences affect the optimal price and lead time decisions, the benefits of dynamic quo- tation, and the optimal mix of spot purchaser and contract customers. These analyses necessitate the computation of expected tardiness of customer orders at the moment cus- tomer enters the system. Hence, in the second part of the dissertation, I develop method- ologies to compute the expected tardiness in multi-class priority queues. For the trivial single class case, a closed formulation is obtained. For the more complex multi-class case, numerical inverse Laplace transformation algorithms are developed. In the last part of the dissertation, I model a decentralized system with two components. Marketing department determines the price quotes with the objective of maximizing revenues, and manufacturing department determines the lead time quotes to minimize lateness costs. I discuss the ben- efits of coordinating price and lead time decisions, and develop an incentivization scheme to reduce the negative impacts of lack of coordination.
ContributorsHafizoglu, Ahmet Baykal (Author) / Gel, Esma S (Thesis advisor) / Villalobos, Jesus R (Committee member) / Mirchandani, Pitu (Committee member) / Keskinocak, Pinar (Committee member) / Runger, George C. (Committee member) / Arizona State University (Publisher)
Created2012
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
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
The Pearson and likelihood ratio statistics are well-known in goodness-of-fit testing and are commonly used for models applied to multinomial count data. When data are from a table formed by the cross-classification of a large number of variables, these goodness-of-fit statistics may have lower power and inaccurate Type I error rate due to sparseness. Pearson's statistic can be decomposed into orthogonal components associated with the marginal distributions of observed variables, and an omnibus fit statistic can be obtained as a sum of these components. When the statistic is a sum of components for lower-order marginals, it has good performance for Type I error rate and statistical power even when applied to a sparse table. In this dissertation, goodness-of-fit statistics using orthogonal components based on second- third- and fourth-order marginals were examined. If lack-of-fit is present in higher-order marginals, then a test that incorporates the higher-order marginals may have a higher power than a test that incorporates only first- and/or second-order marginals. To this end, two new statistics based on the orthogonal components of Pearson's chi-square that incorporate third- and fourth-order marginals were developed, and the Type I error, empirical power, and asymptotic power under different sparseness conditions were investigated. Individual orthogonal components as test statistics to identify lack-of-fit were also studied. The performance of individual orthogonal components to other popular lack-of-fit statistics were also compared. When the number of manifest variables becomes larger than 20, most of the statistics based on marginal distributions have limitations in terms of computer resources and CPU time. Under this problem, when the number manifest variables is larger than or equal to 20, the performance of a bootstrap based method to obtain p-values for Pearson-Fisher statistic, fit to confirmatory dichotomous variable factor analysis model, and the performance of Tollenaar and Mooijaart (2003) statistic were investigated.
ContributorsDassanayake, Mudiyanselage Maduranga Kasun (Author) / Reiser, Mark R. (Thesis advisor) / Kao, Ming-Hung (Committee member) / Wilson, Jeffrey (Committee member) / St. Louis, Robert (Committee member) / Kamarianakis, Ioannis (Committee member) / Arizona State University (Publisher)
Created2018
Description
The recent technological advances enable the collection of various complex, heterogeneous and high-dimensional data in biomedical domains. The increasing availability of the high-dimensional biomedical data creates the needs of new machine learning models for effective data analysis and knowledge discovery. This dissertation introduces several unsupervised and supervised methods to help understand the data, discover the patterns and improve the decision making. All the proposed methods can generalize to other industrial fields.
The first topic of this dissertation focuses on the data clustering. Data clustering is often the first step for analyzing a dataset without the label information. Clustering high-dimensional data with mixed categorical and numeric attributes remains a challenging, yet important task. A clustering algorithm based on tree ensembles, CRAFTER, is proposed to tackle this task in a scalable manner.
The second part of this dissertation aims to develop data representation methods for genome sequencing data, a special type of high-dimensional data in the biomedical domain. The proposed data representation method, Bag-of-Segments, can summarize the key characteristics of the genome sequence into a small number of features with good interpretability.
The third part of this dissertation introduces an end-to-end deep neural network model, GCRNN, for time series classification with emphasis on both the accuracy and the interpretation. GCRNN contains a convolutional network component to extract high-level features, and a recurrent network component to enhance the modeling of the temporal characteristics. A feed-forward fully connected network with the sparse group lasso regularization is used to generate the final classification and provide good interpretability.
The last topic centers around the dimensionality reduction methods for time series data. A good dimensionality reduction method is important for the storage, decision making and pattern visualization for time series data. The CRNN autoencoder is proposed to not only achieve low reconstruction error, but also generate discriminative features. A variational version of this autoencoder has great potential for applications such as anomaly detection and process control.
The first topic of this dissertation focuses on the data clustering. Data clustering is often the first step for analyzing a dataset without the label information. Clustering high-dimensional data with mixed categorical and numeric attributes remains a challenging, yet important task. A clustering algorithm based on tree ensembles, CRAFTER, is proposed to tackle this task in a scalable manner.
The second part of this dissertation aims to develop data representation methods for genome sequencing data, a special type of high-dimensional data in the biomedical domain. The proposed data representation method, Bag-of-Segments, can summarize the key characteristics of the genome sequence into a small number of features with good interpretability.
The third part of this dissertation introduces an end-to-end deep neural network model, GCRNN, for time series classification with emphasis on both the accuracy and the interpretation. GCRNN contains a convolutional network component to extract high-level features, and a recurrent network component to enhance the modeling of the temporal characteristics. A feed-forward fully connected network with the sparse group lasso regularization is used to generate the final classification and provide good interpretability.
The last topic centers around the dimensionality reduction methods for time series data. A good dimensionality reduction method is important for the storage, decision making and pattern visualization for time series data. The CRNN autoencoder is proposed to not only achieve low reconstruction error, but also generate discriminative features. A variational version of this autoencoder has great potential for applications such as anomaly detection and process control.
ContributorsLin, Sangdi (Author) / Runger, George C. (Thesis advisor) / Kocher, Jean-Pierre A (Committee member) / Pan, Rong (Committee member) / Escobedo, Adolfo R. (Committee member) / Arizona State University (Publisher)
Created2018
Description
Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented.
ContributorsYu, Wanchunzi (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Committee member) / Kao, Ming-Hung (Committee member) / St Louis, Robert D (Committee member) / Wilson, Jeffrey (Committee member) / Arizona State University (Publisher)
Created2015