In this dissertation I investigate several topics in the field of nonparametric econometrics. In chapter II, we consider the problem of estimating a nonparametric regression model with only categorical regressors. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values thereby smoothing out the irrelevant regressors. In chapter III, we consider the problem of estimating a joint distribution defined over a set of discrete variables. We use a smoothing kernel estimator to estimate the joint distribution, allowing for the case in which some of the discrete variables are uniformly distributed, and explicitly address the vector-valued smoothing parameter case due to its practical relevance. We show that the cross-validated smoothing parameters differ in their asymptotic behavior depending on whether a variable is uniformly distributed or not. In chapter IV, we consider a k-n-n estimation of regression function with k selected by a cross validation method. We consider both the local constant and local linear cases. In both cases, the convergence rate of of the cross validated k is established. In chapter V, we consider nonparametric estimation of regression functions with mixed categorical and continuous data. The smoothing parameters in the model are selected by a cross-validation method. The uniform convergence rate of the kernel regression function estimator function with weakly dependent data is derived.

A generalisation of Q-sets (and maps between them) called quantal sets, is introduced for an idempotent quantale Q. It turns out that subsets of a quantal set do not correspond bijectively with its subobjects. Quantal sets are shown to form a topos with an internal quantale which classifies subsets. We define appropriate notions of complete quantal set, presheaf and sheaf over Q, and show that the categories of quantal sets and sheaves over Q are equivalent. Based on subsets of quantal sets, a category is constructed in which the properties of the &-operation of Q are reflected. Finally, we construct a bicategory m from Q, and define a concept of quasi-symmetric E-category; it is proved that complete quantal sets may be characterised as quasi-symmetric E-categories satisfying additional properties.

Automated machine learning (AutoML) has become a new trend which is the process of automating the complete pipeline from the raw dataset to the development of machine learning model. It not only can relief data scientists' works but also allows non-experts to finish the jobs without solid knowledge and understanding of statistical inference and machine learning. One limitation of AutoML framework is the data quality differs significantly batch by batch. Consequently, fitted model quality for some batches of data can be very poor due to distribution shift for some numerical predictors. In this dissertation, we develop an intelligent binning to resolve this problem. In addition, various regularized regression classifiers (RRCs) including Ridge, Lasso and Elastic Net regression have been tested to enhance model performance further after binning. We focus on the binary classification problem and have developed an AutoML framework using Python to handle the entire data preparation process including data partition and intelligent binning. This system has been tested extensively by simulations and real datasets analyses and the results have shown that (1) All the models perform better with intelligent binding for both balanced and imbalance binary classification problem. (2) Regression-based methods are more sensitive than tree-based methods using intelligent binning. RRCs can work better than other tree methods by using intelligent binning technique. (3) Weighted RRC can obtain the best results compared to other methods. (4) Our framework is an effective and reliable tool to conduct AutoML.

Understanding data on novel coronavirus (COVID-19) pandemic, and modeling such data over time are crucial for decision making at managing, fighting, and controlling the spread of this emerging disease. This thesis work looks at some aspects of exploratory analysis and modeling of COVID-19 data obtained from the Florida Department of Health (FDOH). In particular, the present work is devoted to data collection, preparation, description, and modeling of COVID-19 cases and deaths reported by FDOH between March 12, 2020, and April 30, 2021. For modeling data on both cases and deaths, this thesis utilized an autoregressive integrated moving average (ARIMA) times series model. The "IDENTIFY" statement of SAS PROC ARIMA suggests a few competing models with suggested values of the parameter p (the order of the Autoregressive model), d (the order of the differencing), and q (the order of the Moving Average model). All suggested models are then compared using AIC (Akaike Information Criterion), SBC (Schwarz Bayes Criterion), and MAE (Mean Absolute Error) values, and the best-fitting models are then chosen with smaller values of the above model comparison criteria. To evaluate the performance of the model selected under this modeling approach, the procedure is repeated using the first six month's data and forecasting the next 7 days data, nine month's data and forecasting the next 7 days data, and then all reported FDOH data from March 12, 2020, to April 30, 2021, and forecasting the future data. The findings of exploratory data analysis that suggests higher COVID-19 cases for females compared to males and higher male deaths compared to females are taken into consideration by evaluating the performance of final models by gender for both cases and deaths' data reported by FDOH. The gender-specific models appear to be better under model comparison criteria Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) compared to models based on gender aggregated data. It is observed that the fitted models reasonably predicted the future numbers of confirmed cases and deaths. Given similarities in reported COVID-19 data, the proposed modeling approach can be applied to data in the USA and many other States, and countries around the world.

Recent advances in technology have increased the need for using simulation models to analyze tasks and obtain human performance data. A variety of task analysis approaches and tools have been proposed and developed over the years. Over 100 task analysis methods have been reported in the literature. However, most of the developed methods and tools allow for representation of the static aspects of the tasks performed by expert system-driven human operators, neglecting aspects of the work environment, i.e. physical layout, and dynamic aspects of the task. The use of simulation can help face the new challenges in the field of task analysis as it allows for simulation of the dynamic aspects of the tasks, the humans performing them, and their locations in the environment. Modeling and/or simulation task analysis tools and techniques have been proven to be effective in task analysis, workload, and human reliability assessment. However, most of the existing task analysis simulation models and tools lack features that allow for consideration of errors, workload, level of operator's expertise and skills, among others. In addition, the current task analysis simulation tools require basic training on the tool to allow for modeling the flow of task analysis process and/or error and workload assessment. The modeling process is usually achieved using drag and drop functionality and, in some cases, programming skills. This research focuses on automating the modeling process and simulating individuals (or groups of individuals) performing tasks in a dynamic work environment in any domain. The main objective of this research is to develop a universal tool that allows for modeling and simulation of task analysis models in a short amount of time with limited need for training or knowledge of modeling and simulation theory. A Universal Task Analysis Simulation Modeling (UTASiMo) tool can be used for automatically generating simulation models that analyze the tasks performed by human operators. UTASiMo is a multi-method modeling and simulation tool developed as a combination of agent-based, discrete event, and system dynamics simulation models. A generic multi-method modeling and simulation framework, named 3M&S Framework, as well as the Unified Modeling Language have been used for the design of the conceptual model and the implementation of the simulation tool. UTASiMo-generated models are dynamically created during run-time based on user inputs. The simulation results include estimations of operator workload, task completion time, and probability of human errors based on human operator variability and task structure.

Attributed graph is a powerful tool to model real-life systems which exist in many domains such as social science, biology, e-commerce, etc. The behaviors of those systems are mostly defined by or dependent on their corresponding network structures. Graph analysis has become an important line of research due to the rapid integration of such systems into every aspect of human life and the profound impact they have on human behaviors. Graph structured data contains a rich amount of information from the network connectivity and the supplementary input features of nodes. Machine learning algorithms or traditional network science tools have limitation in their capability to make use of both network topology and node features. Graph Neural Networks (GNNs) provide an efficient framework combining both sources of information to produce accurate prediction for a wide range of tasks including node classification, link prediction, etc. The exponential growth of graph datasets drives the development of complex GNN models causing concerns about processing time and interpretability of the result. Another issue arises from the cost and limitation of collecting a large amount of annotated data for training deep learning GNN models. Apart from sampling issue, the existence of anomaly entities in the data might degrade the quality of the fitted models. In this dissertation, we propose novel techniques and strategies to overcome the above challenges. First, we present a flexible regularization scheme applied to the Simple Graph Convolution (SGC). The proposed framework inherits fast and efficient properties of SGC while rendering a sparse set of fitted parameter vectors, facilitating the identification of important input features. Next, we examine efficient procedures for collecting training samples and develop indicative measures as well as quantitative guidelines to assist practitioners in choosing the optimal sampling strategy to obtain data. We then improve upon an existing GNN model for the anomaly detection task. Our proposed framework achieves better accuracy and reliability. Lastly, we experiment with adapting the flexible regularization mechanism to link prediction task.

Sequential multiple change point detection concerns the identification of multiple points in time where the systematic behavior of a statistical process changes. A special case of this problem, called online anomaly detection, occurs when the goal is to detect the first change and then signal an alert to an analyst for further investigation. This dissertation concerns the use of methods based on kernel functions and support vectors to detect changes. A variety of support vector-based methods are considered, but the primary focus concerns Least Squares Support Vector Data Description (LS-SVDD). LS-SVDD constructs a hypersphere in a kernel space to bound a set of multivariate vectors using a closed-form solution. The mathematical tractability of the LS-SVDD facilitates closed-form updates for the LS-SVDD Lagrange multipliers. The update formulae concern either adding or removing a block of observations from an existing LS-SVDD description, respectively, and thus LS-SVDD can be constructed or updated sequentially which makes it attractive for online problems with sequential data streams. LS-SVDD is applied to a variety of scenarios including online anomaly detection and sequential multiple change point detection.

Philosophiae Doctor - PhD / In a category C with a proper (E; M)-factorization system for morphisms, we further investigate categorical topogenous structures and demonstrate their prominent role played in providing a uni ed approach to the theory of closure, interior and neighbourhood operators. We then introduce and study an abstract notion of C asz ar's syntopogenous structure which provides a convenient setting to investigate a quasi-uniformity on a category. We demonstrate that a quasi-uniformity is a family of categorical closure operators. In particular, it is shown that every idempotent closure operator is a base for a quasi-uniformity. This leads us to prove that for any idempotent closure operator c (interior i) on C there is at least a transitive quasi-uniformity U on C compatible with c (i). Various notions of completeness of objects and precompactness with respect to the quasi-uniformity de ned in a natural way are studied. The great relationship between quasi-uniformities and closure operators in a category inspires the investigation of categorical quasi-uniform structures induced by functors. We introduce the continuity of a C-morphism with respect to two syntopogenous structures (in particular with respect to two quasi-uniformities) and utilize it to investigate the quasiuniformities induced by pointed and copointed endofunctors. Amongst other things, it is shown that every quasi-uniformity on a re ective subcategory of C can be lifted to a coarsest quasi-uniformity on C for which every re ection morphism is continuous. The notion of continuity of functors between categories endowed with xed quasi-uniform structures is also introduced and used to describe the quasi-uniform structures induced by an M- bration and a functor having a right adjoint.

In this thesis, tools of categorical quantum mechanics are used to explain natural language from a cognitive point of view. Categories of generalized relations are developed for the task, examples are provided, and languages that are particularly tricky to describe using this approach are taken into consideration.

In this paper I put forth three criticisms against McDowell account of the idea that moral requirements are categorical imperatives. I argue that McDowell’s account fails as a defense of Kant’s doctrine for at least three reasons. First, McDowell claims that agents can appeal to experience in order to formulate and recognize categorical imperatives. However, Kant strongly disagrees with this claim, explicitly claiming that moral requirements cannot be derived from experience. Second, McDowell argues that the virtuous agent will not experience inner conflict when motivating herself to act virtuously, but inner conflict plays a central role in Kant’s picture of moral motivation and virtue. Third, McDowell does not account for how the moral law serves as a necessary incentive to moral action through the a priori feeling of respect. Finally, I suggest that my criticisms cast doubt on the validity of McDowell’s account, and provide insights into some criteria that an account must meet if it is to be a proper defense of Kant’s doctrine of moral requirements as categorical imperatives.