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- Genre: Academic theses
- Creators: Lan, Shiwei
- Creators: Young, Dennis
- Creators: Zhou, Shuang
Description
This work presents two complementary studies that propose heuristic methods to capture characteristics of data using the ensemble learning method of random forest. The first study is motivated by the problem in education of determining teacher effectiveness in student achievement. Value-added models (VAMs), constructed as linear mixed models, use students’ test scores as outcome variables and teachers’ contributions as random effects to ascribe changes in student performance to the teachers who have taught them. The VAMs teacher score is the empirical best linear unbiased predictor (EBLUP). This approach is limited by the adequacy of the assumed model specification with respect to the unknown underlying model. In that regard, this study proposes alternative ways to rank teacher effects that are not dependent on a given model by introducing two variable importance measures (VIMs), the node-proportion and the covariate-proportion. These VIMs are novel because they take into account the final configuration of the terminal nodes in the constitutive trees in a random forest. In a simulation study, under a variety of conditions, true rankings of teacher effects are compared with estimated rankings obtained using three sources: the newly proposed VIMs, existing VIMs, and EBLUPs from the assumed linear model specification. The newly proposed VIMs outperform all others in various scenarios where the model was misspecified. The second study develops two novel interaction measures. These measures could be used within but are not restricted to the VAM framework. The distribution-based measure is constructed to identify interactions in a general setting where a model specification is not assumed in advance. In turn, the mean-based measure is built to estimate interactions when the model specification is assumed to be linear. Both measures are unique in their construction; they take into account not only the outcome values, but also the internal structure of the trees in a random forest. In a separate simulation study, under a variety of conditions, the proposed measures are found to identify and estimate second-order interactions.
ContributorsValdivia, Arturo (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Broatch, Jennifer (Committee member) / Arizona State University (Publisher)
Created2013
Description
Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of stream dependence can be missed by each approach because neither one fully addresses the multivariate nature of the accumulated data when generators are run in parallel. This dissertation identifies these potential faults in the parallel testing methodologies of TestU01 and investigates two different methods to better detect inter-stream dependencies: correlation motivated multivariate tests and vector time series based tests. These methods have been implemented in an extension to TestU01 built in C++ and the unique aspects of this extension are discussed. A variety of different generation scenarios are then examined using the TestU01 suite in concert with the extension. This enhanced software package is found to better detect certain forms of inter-stream dependencies than the original TestU01 suites of tests.
ContributorsIsmay, Chester (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
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
Some topics concerning the singular value decomposition and generalized singular value decomposition
Description
This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
ContributorsHuang, Qing (Author) / Eubank, Randall (Thesis advisor) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Gelb, Anne (Committee member) / Young, Dennis (Committee member) / Arizona State University (Publisher)
Created2012
Description
A least total area of triangle method was proposed by Teissier (1948) for fitting a straight line to data from a pair of variables without treating either variable as the dependent variable while allowing each of the variables to have measurement errors. This method is commonly called Reduced Major Axis (RMA) regression and is often used instead of Ordinary Least Squares (OLS) regression. Results for confidence intervals, hypothesis testing and asymptotic distributions of coefficient estimates in the bivariate case are reviewed. A generalization of RMA to more than two variables for fitting a plane to data is obtained by minimizing the sum of a function of the volumes obtained by drawing, from each data point, lines parallel to each coordinate axis to the fitted plane (Draper and Yang 1997; Goodman and Tofallis 2003). Generalized RMA results for the multivariate case obtained by Draper and Yang (1997) are reviewed and some investigations of multivariate RMA are given. A linear model is proposed that does not specify a dependent variable and allows for errors in the measurement of each variable. Coefficients in the model are estimated by minimization of the function of the volumes previously mentioned. Methods for obtaining coefficient estimates are discussed and simulations are used to investigate the distribution of coefficient estimates. The effects of sample size, sampling error and correlation among variables on the estimates are studied. Bootstrap methods are used to obtain confidence intervals for model coefficients. Residual analysis is considered for assessing model assumptions. Outlier and influential case diagnostics are developed and a forward selection method is proposed for subset selection of model variables. A real data example is provided that uses the methods developed. Topics for further research are discussed.
ContributorsLi, Jingjin (Author) / Young, Dennis (Thesis advisor) / Eubank, Randall (Thesis advisor) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2012
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
Longitudinal data involving multiple subjects is quite popular in medical and social science areas. I consider generalized linear mixed models (GLMMs) applied to such longitudinal data, and the optimal design searching problem under such models. In this case, based on optimal design theory, the optimality criteria depend on the estimated parameters, which leads to local optimality. Moreover, the information matrix under a GLMM doesn't have a closed-form expression. My dissertation includes three topics related to this design problem. The first part is searching for locally optimal designs under GLMMs with longitudinal data. I apply penalized quasi-likelihood (PQL) method to approximate the information matrix and compare several approximations to show the superiority of PQL over other approximations. Under different local parameters and design restrictions, locally D- and A- optimal designs are constructed based on the approximation. An interesting finding is that locally optimal designs sometimes apply different designs to different subjects. Finally, the robustness of these locally optimal designs is discussed. In the second part, an unknown observational covariate is added to the previous model. With an unknown observational variable in the experiment, expected optimality criteria are considered. Under different assumptions of the unknown variable and parameter settings, locally optimal designs are constructed and discussed. In the last part, Bayesian optimal designs are considered under logistic mixed models. Considering different priors of the local parameters, Bayesian optimal designs are generated. Bayesian design under such a model is usually expensive in time. The running time in this dissertation is optimized to an acceptable amount with accurate results. I also discuss the robustness of these Bayesian optimal designs, which is the motivation of applying such an approach.
ContributorsShi, Yao (Author) / Stufken, John (Thesis advisor) / Kao, Ming-Hung (Thesis advisor) / Lan, Shiwei (Committee member) / Pan, Rong (Committee member) / Reiser, Mark (Committee member) / Arizona State University (Publisher)
Created2022
Description
This dissertation comprises two projects: (i) Multiple testing of local maxima for detection of peaks and change points with non-stationary noise, and (ii) Height distributions of critical points of smooth isotropic Gaussian fields: computations, simulations and asymptotics. The first project introduces a topological multiple testing method for one-dimensional domains to detect signals in the presence of non-stationary Gaussian noise. The approach involves conducting tests at local maxima based on two observation conditions: (i) the noise is smooth with unit variance and (ii) the noise is not smooth where kernel smoothing is applied to increase the signal-to-noise ratio (SNR). The smoothed signals are then standardized, which ensures that the variance of the new sequence's noise becomes one, making it possible to calculate $p$-values for all local maxima using random field theory. Assuming unimodal true signals with finite support and non-stationary Gaussian noise that can be repeatedly observed. The algorithm introduced in this work, demonstrates asymptotic strong control of the False Discovery Rate (FDR) and power consistency as the number of sequence repetitions and signal strength increase. Simulations indicate that FDR levels can also be controlled under non-asymptotic conditions with finite repetitions. The application of this algorithm to change point detection also guarantees FDR control and power consistency. The second project focuses on investigating the explicit and asymptotic height densities of critical points of smooth isotropic Gaussian random fields on both Euclidean space and spheres.The formulae are based on characterizing the distribution of the Hessian of the Gaussian field using the Gaussian orthogonally invariant (GOI) matrices and the Gaussian orthogonal ensemble (GOE) matrices, which are special cases of GOI matrices. However, as the dimension increases, calculating explicit formulae becomes computationally challenging. The project includes two simulation methods for these distributions. Additionally, asymptotic distributions are obtained by utilizing the asymptotic distribution of the eigenvalues (excluding the maximum eigenvalues) of the GOE matrix for large dimensions. However, when it comes to the maximum eigenvalue, the Tracy-Widom distribution is utilized. Simulation results demonstrate the close approximation between the asymptotic distribution and the real distribution when $N$ is sufficiently large.
Contributorsgu, shuang (Author) / Cheng, Dan (Thesis advisor) / Lopes, Hedibert (Committee member) / Fricks, John (Committee member) / Lan, Shiwei (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2023
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