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- All Subjects: Statistics
- Genre: Academic theses
- Creators: Runger, George C.

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…

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.

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…

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.

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…

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.

Anomaly is a deviation from the normal behavior of the system and anomaly detection techniques try to identify unusual instances based on deviation from the normal data. In this work, I propose a machine-learning algorithm, referred to as Artificial Contrasts, for anomaly detection in categorical data in which neither the…

Anomaly is a deviation from the normal behavior of the system and anomaly detection techniques try to identify unusual instances based on deviation from the normal data. In this work, I propose a machine-learning algorithm, referred to as Artificial Contrasts, for anomaly detection in categorical data in which neither the dimension, the specific attributes involved, nor the form of the pattern is known a priori. I use RandomForest (RF) technique as an effective learner for artificial contrast. RF is a powerful algorithm that can handle relations of attributes in high dimensional data and detect anomalies while providing probability estimates for risk decisions.

I apply the model to two simulated data sets and one real data set. The model was able to detect anomalies with a very high accuracy. Finally, by comparing the proposed model with other models in the literature, I demonstrate superior performance of the proposed model.

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…

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.

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…

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.

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…

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.

Spatial regression is one of the central topics in spatial statistics. Based on the goals, interpretation or prediction, spatial regression models can be classified into two categories, linear mixed regression models and nonlinear regression models. This dissertation explored these models and their real world applications. New methods and models were…

Spatial regression is one of the central topics in spatial statistics. Based on the goals, interpretation or prediction, spatial regression models can be classified into two categories, linear mixed regression models and nonlinear regression models. This dissertation explored these models and their real world applications. New methods and models were proposed to overcome the challenges in practice. There are three major parts in the dissertation.

In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution.

In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine.

A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data.

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 hel…

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.

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.…

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).