This dissertation is about a particular style of research. The philosophy of this style is that in order to scientifically understand deep learning, it is fruitful to investigate what happens when neural networks are trained on simple, mathematically well-defined tasks. Even though the training data is simple, the training algorithm can end up…

While large language models (LLMs) continue to grow in scale and gain new zero-shot capabilities, their performance for languages beyond English increasingly lags behind. This gap is due to the "curse of multilinguality," where multilingual language models perform worse on individual languages than a monolingual model trained on that…

The research in this dissertation consists of two parts: An active learning algorithm for hierarchical labels and an embedding-based retrieval algorithm. In the first part, we present a new approach for learning hierarchically decomposable concepts. The approach learns a high-level classifier (e.g., location vs. non-location) by separately…

The essence of human intelligence lies in its ability to learn continuously, accumulating past knowledge to aid in future learning and problem-solving endeavors. In contrast, the current machine learning paradigm often operates in isolation, lacking the capacity for continual learning and adaptation. This deficiency becomes apparent in the face of…

Whether machine learning algorithms effectively predict college students' course outcomes using learning management system data is unknown. Identifying students who will have a poor outcome can help institutions plan future budgets and allocate resources to create interventions for underachieving students. Therefore, knowing the effectiveness of…

Every year, the national high school graduation rate is declining and impacting the number of students applying to colleges. Moreover, the majority of students are applying to more than one college. This makes a lot of colleges to be highly competitive in student recruitment for enrollment and thus, the necessity for institutions to anticipate…

With the rise in popularity of social media and e-commerce platforms, "discrete math" is at the heart of our online experiences, playing a front-end role in the recommendation of what to click, watch, or buy, or who to follow or friend, as well as a back-end role in data storage, access, and transfer. This thesis focuses on two such…

Teacher turnover continues to be a significant problem in the United States. Teacher turnover is expensive because it costs money to continue recruiting, hiring, and training new teachers to replace those leaving (Carver-Thomas & Darling-Hammond, 2017). Most important though, teacher turnover hurts student achievement and success (Sorensen…

Graph Signal Processing (GSP) plays a crucial role in addressing the growing need for information processing across networks, especially in tasks like supervised classification. However, the success of GSP in such tasks hinges on accurately identifying the underlying relational structures, which are often not readily available and must be inferred…

Bayesian network is a probabilistic graphical model that has wide applications in various domains due to its peculiarity of knowledge representation and reasoning under uncertainty. This research aims at Bayesian network structure learning and how the learned model can be used for reasoning. Learning the structure of Bayesian network from data is…

The past thirty years have shown a rise in models of language acquisition in which the state of the learner is characterized as a probability distribution over a set of non-stochastic grammars. In recent years, increasingly powerful models have been constructed as earlier models have failed to generalize well to increasingly complex and realistic…

To meet the national and international call for creative and innovative engineers, many engineering departments and classrooms are striving to create more authentic learning spaces where students are actively engaging with design and innovation activities. For example, one model for teaching innovation is Innovation-Based Learning (IBL) where…

Since near the very beginning of electronic computing, Monte Carlo particle transport has been a fundamental approach for solving computational physics problems. Due to the high computational demands and inherently parallel nature of these applications, Monte Carlo transport applications are often performed in the supercomputing environment. That…

Linguistic meaning is generated by the mind and can be expressed in multiple languages. One may assume that equivalent texts/utterances in two languages by means of translation generate equivalent meanings in their readers/hearers. This follows if we assume that meaning calculated from the linguistic input is solely objective in nature. However,…

This thesis studies four independent resource allocation problems with different assumptions on information available to the central planner, and strategic considerations of the agents present in the system. We start off with an online, non-strategic agents setting in Chapter 1, where we study the dynamic pricing and learning problem under the…