Computational learning theory studies the design and analysis of learning algorithms, and it is integral to the foundation of machine learning. In the modern era, classical computational learning theory is growingly unable to catch up with new practical demands. In particular, problems arise in the following aspects: i). "scalability":…

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, interpreting these functional principal components (PCs) can sometimes be challenging due to issues such as roughness and sparsity. In this dissertation,…

This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

This dissertation used synthetic datasets, semi-synthetic datasets, and a real-world dataset from an educational intervention to compare the performance of 15 machine learning and multiple imputation methods to estimate the individual treatment effect (ITE). In addition, it examined the performance of five evaluation metrics that can be used to…

Multidimensional Item Response Theory (MIRT) has been widely used in educational and psychological assessments. It estimates multiple constructs simultaneously and models the correlations among latent constructs. While it provides more accurate results, the unidimensional IRT model is still dominant in real applications. One major reason is that…

This dissertation studies the advancement of consensus-aware technologies in the context of collective decision-making, focusing on the integration of these technologies into information systems to effectively represent, detect, and characterize consensus among people and other agents. Despite the proven value of collective intelligence in…

This dissertation address two significant challenges in the causal inference workflow for Big Observational Data. The first is designing Big Observational Data with high-dimensional and heterogeneous covariates. The second is performing uncertainty quantification for estimates of causal estimands that are obtained from the application of black box…

This study was conducted to further research into the impact of student-group item parameter drift (SIPD) --referred to as subpopulation item parameter drift in previous research-- on ability estimates and proficiency classification accuracy when occurring in the discrimination parameter of a 2-PL item response theory (IRT) model. Using Monte…

This dissertation examines the response of a group of educators to a state mandate to integrate computational thinking (CT) into all levels of the curriculum. It explores the historical development of CT and its significance within the broader context of Science, Technology, Engineering, and Mathematics education, emphasizing the rapid growth and…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

The concept of computational thinking (CT) has become more prevalent across the engineering education research and teaching landscape. Yet much of the research to date has been more definitional and has not offered many ways to convert CT theory to practice. One prominent set of tools used across engineering disciplines is modeling and simulation,…

Computational thinking (CT) is recognized as an essential and universally applicable skill for all disciplines (Wing, 2006; Bundy, 2007). Proponents of CT acknowledge that it is integral to fostering 21st century skills such as problem-solving and higher-order thinking (Barr & Stephenson, 2011; Wing, 2006). Educational robotics activities have…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

Once research questions are posed, researchers must answer many a priori questions regarding research design before analysis can be performed and any conclusions can be made, including sample selection criteria, data collection method, model specification, analysis and estimation technique. The choices made by researchers along this forking path…

Speech is a complex, redundant and variable signal happening in a noisy and ever changing world. How do listeners navigate these complex auditory scenes and continuously and effortlessly understand most of the speakers around them? Studies show that listeners can quickly adapt to new situations, accents and even to distorted speech. Although prior…