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Geometry processing holds a foundational position within the realm of computer graphics, with advancements in this field regularly published at SIGGRAPH annually. The journey from writing the paper to implementing the algorithms is a meticulous and error-prone process, demanding significant dedication and attention to detail. Authors frequently encounter challenges, including inadvertent typos within formulas that can introduce discrepancies between the paper and the actual code. This discrepancy can pose a significant hurdle for readers, especially new researchers and graduate students, aiming to reproduce the results. Even when authors release their code, readers may desire versions in their preferred programming languages. My dissertation focus is on mitigating challenges faced by researchers throughout scientific computing according to a suite of domain-specific languages (DSLs). The goal is to enable authors to easily try new research ideas and compose papers with these DSLs, automating the generation of algorithmic code across diverse backend languages like C++, Python, and MATLAB. I have developed three instrumental tools with my collaborators to handle those sections in papers: I[heart]LA for compiling the implementation, I[heart]MESH for compiling the discretization, and H[heart]rtDown for compiling linear algebra papers into interactive documents. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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 rapidly evolving artificial intelligence (AI) technologies, particularly large language models (LLMs), where incremental training remains a challenge. Continual learning (CL), also known as lifelong learning, is indispensable for truly intelligent systems, especially in dynamic environments where constant adaptation is necessary. This dissertation explores recent advancements in continual learning algorithms within the framework of language models. We first introduce the settings, challenges, and general approaches of CL. We then delve into our efforts to achieve both catastrophic forgetting (CF) mitigation and knowledge transfer (KT), and how we apply CL to different stages of language model development, including pre-training and end-task adaptation. With the aid of continual learning, the performance of language models is greatly improved. Finally, we will discuss the opportunities for AI autonomy and open-world continual learning. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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, we establish the theoretical foundations of the penalized MFPCA problem within Hilbert space and propose three novel regularized MFPCA approaches. These approaches utilize eigen decomposition and singular value decomposition (SVD) techniques to enhance the performance of MFPCA by incorporating multiple penalty terms, such as roughness and sparsity penalties. In the first method, a roughness penalty is directly imposed on functional PCs, extending the eigen decomposition problem to a Hilbert space that specifically accounts for the roughness of the functions. A parameter vector is employed as a tuning parameter to regulate the smoothness of each functional variable. Additionally, this method allows for each functional variable to be smoothed on different domains, providing greater flexibility in handling diverse functional data. In the other two methods, we establish a mathematical foundation for penalized functional SVD to address the regularized MFPCA problem. Within the functional SVD framework, we propose iterative power algorithms that offer both the flexibility to assign unique tuning parameters for each functional PC and computational efficiency. Moreover, the functional SVD approach allows for the straightforward and simultaneous incorporation of various penalties, such as smoothing and sparsity, each serving a distinct purpose. Additionally, our functional SVD approach introduces an innovative form of sparsity within PC scores, which proves beneficial for obtaining more informative PCs. Similar to the first approach, these two methods also allow each functional variable to be defined on different domains, providing greater flexibility in data analysis. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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 the parameter estimation is still challenging because of intractable multidimensional integrals of the likelihood, especially in high dimensions. Several algorithms have been proposed to address the issue, such as adaptive Gaussian quadrature methods, Laplace approximations, and stochastic methods. However, the state-of-the-art algorithms are still time-consuming, especially when the number of latent traits exceeds 5. Recently, the Gaussian variational Expectation Maximization (GVEM) algorithm (Cho et al., 2021) was proposed as an alternative for further improving computational efficiency and estimation accuracy. The general framework allows the closed-form solutions for the expectation-maximization process by introducing a variational lower bound of the likelihood function. Although prior studies have demonstrated the superiority of the GVEM algorithm over the widely used Metropolis-Hastings Robbins-Monro algorithm (MH-RM) under various conditions, its performance across diverse practical contexts remains relatively unexplored. For instance, there is an immense need for further investigation into the robustness of the GVEM framework across various missing data scenarios. Additionally, efforts should be directed towards devising methods for estimating standard errors within the GVEM framework. Moreover, the development of an R package to facilitate the application of the GVEM algorithm would significantly augment its accessibility and utility. The purpose of this dissertation is to extend the applicability of the GVEM algorithm and investigate its performance in diverse scenarios. In the second chapter, a modified GVEM algorithm was proposed by adding the bootstrap bias correction step and denoted it as GVEM-BS. A series of simulation studies and real data analysis were conducted to compare GVEM-BS to MH-RM in terms of estimation precision under different missing data scenarios and assessment designs. The results demonstrated the robustness and precision of GVEMBS in the context of high missing proportions, especially for missing at completely random conditions. When applying the two methods to different assessment designs, both GVEM-BS and MH-RM yielded comparable results. In the third chapter, an updated supplemented expectation maximization (USEM) method and a bootstrap method were proposed for GVEM-based SE estimation. These two methods were compared in terms of SE recovery accuracy. The simulation results demonstrated that the GVEM algorithm with bootstrap and item priors (GVEM-BSP) outperformed the other methods, exhibiting less bias and relative bias for SE estimates under most conditions. Although the GVEM with USEM (GVEM-USEM) was the computationally most efficient method, it yielded an upward bias for SE estimates. In the fourth chapter, an R package, VEMIRT, was introduced by offering users efficient computational tools tailored for high-dimensional data under the GVEM framework. This package facilitates both exploratory and confirmatory analyses through the utilization of GVEM models. Additionally, it enables users to compute standard errors of item parameters and implement corrections such as bootstrap sampling and importance sampling, thereby enhancing the accuracy of estimations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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 applying the algorithms to build models will be helpful in higher education institutions. This study utilizes the probably approximately correct learning theory, which posits machines can learn any concept as long as there is a data set of examples that labels the outcome of the concept, enough examples, and the computation can be completed in a polynomial number of steps. This quantitative comparative study compared four different machine learning algorithms' (naive Bayes, decision tree, neural network, and support vector machine) ability to predict the outcome of students in college courses by training models from learning management system data across two universities. It then measured the predictions of each model at a course level to determine their effectiveness. The results showed that the probably approximately correct learning theory works even in predicting course outcomes, as the decision tree successfully predicted students with poor outcomes with an F1 value above 0.5 and significantly better than the other three algorithms. Future studies can expand on the number of institutions involved in the contributing data and different learning management system data points as they may provide better predictions. Having learned the confidence of the decision tree's ability to predict students that will have poor outcomes, higher education institutions can better plan and allocate resources. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

The field of Data Science has seen rapid growth over the past two decades, with a high demand for people with skills in data analytics, programming, statistics, and ability to visualize, predict from, and otherwise make sense of data. Alongside the rise of various artificial intelligence (AI) and machine learning (ML) applications, we have also witnessed egregious algorithmic biases and harms - from discriminatory outputs of models to reinforcing normative ideals about beauty, gender, race, class, etc. These harms range from high profile cases such as the racial bias embedded in the COMPAS recidivism algorithm, to more insidious cases of algorithmic harm that compound over time with re-traumatizing effects (such as the mental health impacts of recommender systems, social media content organization and the struggle for visibility, and discriminatory content moderation of marginalized individuals). There are various strategies to combat and repair algorithmic harms, ranging from algorithmic audits and fairness metrics to AI Ethics Standards put forth by major institutions and tech companies. However, there is evidence to suggest that current Data Science curricula do not adequately prepare future practitioners to effectively respond to issues of algorithmic harm, "especially" the day-to-day issues that practitioners are likely to face. Through a review of AI Ethics standards and the literature, I devise a set of 9 characterizations of effective AI ethics education: "specific", "prescriptivist", "action-centered", "relatable", "empathetic", "contextual", "expansive", "preventative", and "integrated." The empirical work of this dissertation reveals the value of embedding ethical critique into technical machine learning instruction - demonstrating how teaching AI concepts using cases of algorithmic harm can boost both technical comprehension and ethical considerations [397, 398]. I demonstrate the value of relying on real-world cases and experiences that students already have (such as with hiring/admissions decisions, social media algorithms, or generative AI tools) to boost their learning of both technical and social impact topics. I explore this relationship between personal relatability and experiential learning, demonstrating how to harness students' lived experiences to relate to cases of algorithmic harm and opportunities for repair. My preliminary work also reveals significant "in-group favoritism", suggesting students find AI errors more urgent when they personally relate to them. While this may prove beneficial for engaging underrepresented students in the classroom, it must be paired with empathy-building techniques for students who relate less to cases of algorithmic harm, as well as trauma-informed pedagogical practice. My results also revealed an over-reliance on "life-or-death reasoning" when it came to ethical decision-making, along with organizational and financial pressures that might impede AI professionals from delaying harmful software. This dissertation contributes several strategies to effectively prepare Data Scientists to consider both technical and social aspects of their work, along with empirical results suggesting the benefits of embedded ethics throughout all areas of AI education. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

The present study was conducted to determine how implementing computational thinking (via a proxy in AP Computer Science Principles) into a school's curriculum impacted student proficiency rates on the New York State Geometry Regents. Recent research has suggested that computational thinking is a skill that transcends specific content areas and can influence student learning outcomes across multiple disciplines. By equipping students with these skills, each individual's zone of proximal development may increase, leading to increased learning efficiency. Given the rise of technology and the need for computational literacy, schools are looking to implement courses to help students develop these skills. The target school students were compared to their fellow general education peers in their home and neighboring counties. The target school was unique because students were mandated to take AP Computer Science Principles during their freshman year, while the other students were not. Through multinomial logistic regression, the influence of computational thinking on student proficiency rates was quantified and found to be insignificant. However, the COVID-19 pandemic greatly impacted the students' performance. While the findings were insignificant, the students in the target school were likelier than the other students in their county and the neighboring county to be proficient in Geometry, according to the New York State Education Department's definition of proficiency. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Computational risk detection holds promise for shielding particularly vulnerable groups from online harm. A thorough literature review on real-time computational risk detection methods revealed that most research defined 'real-time' as approaches that analyze content retrospectively as early as possible or as preventive approaches to prevent risks from reaching online environments. This review provided a research agenda to advance the field, highlighting key areas: employing ecologically valid datasets, basing models and features on human understanding, developing responsive models, and evaluating model performance through detection timing and human assessment. This dissertation embraces human-centric methods for both gaining empirical insights into young people's risk experiences online and developing a real-time risk detection system using a dataset of youth social media. By analyzing adolescent posts on an online peer support mental health forum through a mixed-methods approach, it was discovered that online risks faced by youth could be laden by other factors, like mental health issues, suggesting a multidimensional nature of these risks. Leveraging these insights, a statistical model was used to create profiles of youth based on their reported online and offline risks, which were then mapped with their actual online discussions. This empirical study uncovered that approximately 20% of youth fall into the highest risk category, necessitating immediate intervention. Building on this critical finding, the third study of this dissertation introduced a novel algorithmic framework aimed at the 'timely' identification of high-risk situations in youth online interactions. This framework prioritizes the riskiest interactions for high-risk evaluation, rather than uniformly assessing all youth discussions. A notable aspect of this study is the application of reinforcement learning for prioritizing conversations that need urgent attention. This innovative method uses decision-making processes to flag conversations as high or low priority. After training several deep learning models, the study identified Bi-Long Short-Term Memory (Bi-LSTM) networks as the most effective for categorizing conversation priority. The Bi-LSTM model's capability to retain information over long durations is crucial for ongoing online risk monitoring. This dissertation sheds light on crucial factors that enhance the capability to detect risks in real time within private conversations among youth. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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 producing rich, unexpected results; and understanding these results can shed light on fundamental mysteries of high relevance to contemporary deep learning. First, we situate this methodological approach in a broader scientific context, discussing and systematizing the role of "model systems" in science and in the science of deep learning in particular. We then present five intensive case studies, each of which uses a particular combinatorial task as a lens through which to demystify puzzles of deep learning. The combinatorial tasks employed are sparse Boolean functions, sparse parities, learning finite group operations, performing modular addition, and learning Markov chains in-context. Topics of explanatory interest include the inductive biases of the transformer architecture, the phenomenon of emergent capabilities during training, the nuances of deep learning in the presence of statistical-computational gaps, the tradeoffs between different resources of training, the effect of network width on optimization, the relationship between symmetries in training data and harmonic structure in trained networks, the origins of the mechanisms of in-context learning in transformers, and the influence of spurious solutions on optimization. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

The unprecedented racial justice movements of 2020, intensified by George Floyd's tragic murder, catalyzed a global mobilization. This dissertation investigates the intersection of these movements with sociotechnical tools that shaped the movement, focusing on the youth deeply engaged with socioalgorithmic systems and their developmental experiences. Article 1 introduces a theoretical framework to understand modern developmental ecologies through a socioalgorithmic lens. It argues for a pivot in the field of developmental science toward studying the technical facets of digital environments, recognizing algorithms shape not just social interactions and political awareness, but also broader psychological and biological processes. Amid 2020's racial justice uprisings, the article underscores the urgency to investigate how algorithmic mediation influences developmental processes like socio-political identity development, moving beyond the discourse on screen time to scrutinize the roles of technological structures in shaping development. Article 2 presents an empirical study examining the impact of algorithmic bias on Black youth during 2020's tumultuous events. Investigating whether ethnic-racial identity exploration activities buffer against the detrimental mental health effects of algorithmic bias in AI selfie filters, the research integrates racial identity development theories with the psychology of systemic racism. Findings illuminate the complex interactions between socioalgorithmic systems and mental health outcomes in racially marginalized youth, highlighting the non-neutrality of algorithms and their potential to reinforce societal biases. The third article conducts an algorithmic audit of YouTube's search engine regarding Black Lives Matter movement content. This audit critically assesses the digital spaces that youth interact with, analyzing the biases embedded in such search algorithms. The findings suggest although many aspects of the Black Lives Matter movement were represented to be in alignment of the organizer's values, the more radical black liberatory ideas associated with "abolition" are represented more negatively in the content curated by YouTube search. By examining the confluence of algorithmic systems and racial justice activism in 2020, my dissertation advocates for a developmental science paradigm that integrates socioalgorithmic context. It aims to enrich understanding of the digital age's impact on the developmental trajectories of racially marginalized youth and calls for incorporating algorithmic systems analysis into the broader understanding of human development. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

In this dissertation, I present an examination of the economics of education through three chapters. In the first paper, I study the overrepresentation of elite university graduates in senior positions in public administration. Using rich administrative data from Chile, I employ a stacked fuzzy regression discontinuity design to estimate the causal effect of attending elite universities versus non-elite institutions on the likelihood of working in the public sector and attaining top positions within it. The findings suggest that while the observed disparity in top positions within public administration is largely a result of selection rather than inherent advantages of elite education, attending elite universities may enhance social mobility for students from lower socioeconomic backgrounds, particularly within specific majors. In the second paper, my coauthors and I propose an alternative approach using algorithms to predict college readiness and guide course placement. Drawing on experimental data from seven community colleges, the study shows that algorithmic placement increases placement rates into college-level courses without sacrificing pass rates. Moreover, algorithmic placement shows promise in narrowing demographic disparities in placement rates and remedial course enrollment, outperforming traditional placement tests in terms of predictive accuracy while mitigating discrimination. In the final chapter, I explore the relationship between school counselor availability and disciplinary outcomes in middle and high schools across the United States. Leveraging exogenous variations in student-to-counselor ratios driven by state recommendations and mandates, I employ administrative data from 26 states to estimate the causal impact of counselor availability on disciplinary actions such as suspensions, expulsions, and transfers. The results indicate that increased counselor availability reduces school disciplinary actions, with larger effects observed in high schools compared to middle schools. Moreover, speculative analyses suggest that the effectiveness of counselors in mitigating disciplinary issues may be complemented by the overall staffing levels in high schools. This dissertation contributes to our understanding of how educational policies and practices shape individual outcomes and societal inequalities, shedding light on avenues for promoting social mobility, improving educational access and equity, and fostering conducive learning environments. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Human intelligence has the ability to capture abstract concepts from experience and utilize that learned knowledge for adaptation to new situations. Lifelong machine learning aims to achieve those same properties of human intelligence by designing algorithms to learn from a sequence of tasks, extract useful knowledge of previous tasks, and re-use the extracted knowledge to learn new future tasks. Research into lifelong learning has explored various methodologies, including techniques for sharing knowledge across tasks, techniques for maintaining previously acquired skills, and techniques for actively selecting the next task to learn. This dissertation will focus on one theme of lifelong learning: the way knowledge is transferred across tasks via factorization, which breaks down the architecture of neural networks to naturally encode conceptual knowledge. The tensor factorization is capable of discovering abstract but generalizable knowledge from experiences. This dissertation investigates methods to factorize knowledge encoded in neural networks and share the knowledge across multiple tasks, as well as methods to enhance the training of these factorized knowledge transfer mechanisms. This dissertation starts by developing a lifelong learning architecture that utilizes deconvolutional operation to preserve multi-axis features of data. This deconvolution-based factorization architecture empirically shows reduced harmful interference between tasks thanks to sharing abstract knowledge via factorization. The dissertation then studies the importance of transferring the proper level of knowledge in the network for the success of lifelong learning. As a result, an expectation-maximization style algorithm is developed to discover the useful granularity of knowledge to share for each task depending on the given data. This algorithm determines which layers to share while learning tasks in parallel and reduces human intervention in selecting the knowledge transfer architecture for lifelong learning, which is critical for realistic scenarios with complex task relationships. Moreover, it applies to diverse lifelong learning architectures, augmenting existing lifelong learning works. Lastly, the dissertation investigates the use of data programming to extend existing lifelong learning algorithms into semi-supervised settings, tackling the lifelong learning challenge of data annotation. Due to the modularized framework and theoretical guarantees on the quality of generated labels, this framework can be applied to the existing supervised lifelong learning algorithms. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

When the purpose and meaning of grades is not well-defined by an organization, there is a disconnect between curricular/assessment practices and student engagement. This study sought to investigate origins and find solutions in regards to discerning a student's knowledge and mastery of a subject and how this is reflected in the grade, and how grades can be accurately reported. Participants and data collected in Cycle One consisted of professional faculty who shared personal experience with teacher/student/parent perception of grades and their value, and what their curricular and assessments were revealing about student engagement and performance. As consistent themes emerged through interviews and focus groups, Action steps were designed, implemented, and evaluated in Cycle Two to provide a framework for the high school division that would 1) provide clarity and consistency among the faculty, their subject areas, and their departments, and 2) to enhance student engagement through curricular/assessment and grade reporting practices that better reflected the student's knowledge and mastery. A ten-week book study was formed in Cycle Two that challenged current conventions and practices with discussions which evolved from Thomas Guskey's On Your Mark: Challenging the Practices of Grading and Reporting. Ten sessions were developed and co-facilitated by members of the high school faculty/administration at the research site. Evaluating the results of the Action Research study included a thorough assessment of the value of grades and how they are reported at this organization. At the conclusion of the book study, the focus group/participants delivered a formal presentation to the faculty in the high school division which focused on the purpose of grades; the subjectivity of grade reporting; the inaccuracy of percentages and algorithms; the misperception of class ranking; and elements, like behaviors, that obscure the meaning of grades. Participants provided critical feedback throughout the process, and the administration intends to continue honing how faculty arrive at a grade, its intended meaning, its purpose for the student/parent/teacher, and how the organization can better streamline curricular/assessment practices so mastery of a subject matter is clearer. Implications for the organization included an official purpose statement to define the meaning of grades and explain why they are reported; a document that clarifies vocabulary used among all high school subject areas/departments; and, a broad rubric for how to evaluate written assessments. Organizational leaders intend to make other changes that make curricular/assessment and grading practices much more meaningful for the student and their educational experience. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Algorithms may be better at prediction than humans in a variety of contexts, but they are not perfect. A deeper understanding of the ways in which educators use and question algorithmic advice within their professional domain is needed. Educators are a particularly unique professional group, in comparison with the other groups studied in the literature, and will likely be the on-the-ground employees expected to integrate algorithmic advice into their pedagogical planning and decision making. This quantitative study used a 2x2 pretest-posttest experimental design to investigate the way that educators used and trusted algorithmic advice for high school science course recommendations, including the way contextual framing and individual-level differences impacted these relationships. Participants were randomly assigned to one of two purpose conditions in a simulation environment designed using the Judge-Advisor System (JAS) paradigm to assess the influence of algorithmic advice. Group comparison and multiple regression techniques were utilized to test hypotheses. Results indicated that approximately 30% of participants did not change their decision at any time and that the remaining 70% tended to not change their decision when given the chance. Additionally, a significant interaction was detected for average confidence change with participants who had more years of teaching experience having higher rates of average confidence change in the positive purpose condition. More research is suggested that investigates the potential for manipulation of educator trust based on a recommendation system's framing and/or marketing. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Human space exploration is entering a new era through the design of missions that venture further from earth for longer durations, such as missions to the Moon and Mars. Mission success during long duration exploration missions (LDEM) requires astronauts to flawlessly execute exceptionally complex skills across a multitude of tasks, presenting new challenges for training. This thesis investigates virtual reality (VR) as a potential platform to support critical skill training and maintenance during LDEM. First, a VR Entry, Descent, and Landing (EDL) training scenario was created to support the investigational aims of this research. EDL represents a highly complex task that requires extensive preflight training and carries extreme consequences of failure if skill is not properly maintained over time. A collection of design objectives drove the development of the training scenario, including complex subtask integration, algorithm facilitation of adaptive difficulty, a sense of immersion and presence, allowing for repeated training without predictability or boredom, and providing feedback to support learning. The EDL task was created in a modular format that allowed for presentation in immersive VR, non-immersive screen, and physical mockup modalities, as well as with static or adaptive difficulty. In the second aim, the EDL task was then investigated in a collection of between-subjects experiments. In the first experiment, results showed promising trends that adaptive VR training supports higher skill gain and less plateau in learning as well as higher average performance when transitioning from virtual to physical task performance. In the second experiment, facilitation with an adaptive algorithm was found to significantly improve task mastery as opposed to self-led difficulty selection or static difficulty training. Next, simplified corollary task training was found to support retention of skill only if the cognitive demands of that simplified task were appropriately mapped to those of the operational task. And finally, just-in-time training was found to be an effect method to mitigate skill loss while preventing the risks of negative training. The work presented in this thesis found that VR is a valuable tool for the maintenance of mission-critical skill during LDEM. However, skill maintenance is best supported through design of VR training that utilizes adaptive algorithms to facilitate learning, presents content with cognitive demands that align to the tasks they seek to train, and when refresher training is administered in a JIT cadence. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Adaptive tutoring systems often model student knowledge in ways that break away from a "one size fits all" approach to learning. Nonetheless, the strengths of these systems can often be limited, as knowledge representations are not easily interpreted by teachers, which make these systems difficult to integrate into pedagogical practices. Fortunately, as researchers, we can still take advantage of the AI in these systems to extend our innovations and address problems of practice. As such, the goal of the present work is to leverage multidimensional representations of knowledge that these systems provide to explore innovations in educational measurement, pedagogical techniques, and practice. I explore these in three studies outlined below. In Study 1 I explore "Innovations in educational measurement" by adopting an alternative perspective to measuring student mathematical ability. In this study I invite the reader to re-conceptualize mathematical ability as a multidimensional construct, which runs counter to long-established tradition in academic measurement and pedagogical practice. In doing so, I compare the variation observed in students' mathematical ability when ability is measured using different metrics that vary in dimensionality. Findings suggest that under a multidimensional view, students (including those who may be traditionally seen as "low-ability") often possess relative strengths when compared to their peers, thus suggesting that categorizations such as low- and high-ability, which are typically used in practice, may be an over simplification. In Study 2 I explore "Innovations in pedagogical techniques" as I present three novel algorithms for grouping students that leverage existing technological AI innovations that model student knowledge across hundreds of mathematical skills. These methods attempt to better align the personalization of a tutoring system with teachers' instructional practices. I evaluate each of the three methods against two alternative baseline methods--one that groups students randomly and one that groups students based on a unidimensional course score. Findings demonstrate that these novel methods, which adopt a multidimensional view of ability, were more capable than the baseline methods at grouping students with similar strengths and weaknesses on a fine-grained skill level. In Study 3 I explore "Innovations in practice" in a research-practice partnership (RPP) with curriculum specialists at a local urban school district in Southern California. Implementation strategies, including curriculum and grouping recommendations were provided to teachers for a summer intervention program. In the spirit of a design-based implementation partnership, strategies and recommendations were formed to meet the needs of partners, while simultaneously attempting to address known problems of practice when implementing a blended learning design in the classroom. In this first cycle of iteration, these attempts were examined through teacher surveys as well as student login and learning data in a tutoring system. Ultimately, these data were used to examine the fidelity of implementation so that findings may inform future iterations of this ongoing partnership. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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": with the massive scales of modern datasets, classical learning algorithms that use polynomial time and store the entire input are no longer efficient; ii). "uncertainty": information nowadays is usually coupled with noise and uncertainty, which renders classical algorithms that assume accurate information unreliable; and iii). "practicality": under the modern context, traditional "negligible" terms in learning theory (e.g., log n factors) can no longer be ignored, and many theoretically-efficient techniques become inapplicable in practice. There are several promising approaches to tackle the above challenges. For scalability, one of the most popular approaches is to study learning algorithms under "sublinear" models, including streaming, sublinear time, and Massively Parallel Computation (MPC) models. Learning algorithms under these models usually use resources substaintially smaller than the input size. For uncertainty, we can look into learning algorithms that naturally take noisy inputs, e.g., algorithms that deal with multi-armed bandits (MABs), or algorithms that operate with randomly corrupted inputs. Finally, for practicality, we can focus on designing algorithms that are easy to implement and aim for algorithms with both theoretical guarantees and experimental performances. In light of the above discussion, this dissertation presents three major areas of study as follows: (1) In Part I, we present recent results in streaming multi-armed bandits, where the arms arrive one by one in a stream, and the algorithm stores a much smaller number of arms than the input. We consider two fundamental learning problems in this model, namely pure exploration and regret minimization. For pure exploration, we give an ultra-efficient algorithm that finds the best arm and stores a single extra arm at any point. The algorithm uses a single pass and the information-theoretically optimal number of arm pulls. Subsequently, under various settings, we characterize the optimal sample-memory-pass trade-offs for pure exploration streaming MABs. For regret minimization, we give the optimal regret bounds for single-pass MABs. Together, these results complete a majority of the picture for classical MABs problems under the memory-constraint setting; (2) In part II, we study graph clustering in sublinear settings. We consider two important problems in practice: correlation clustering and hierarchical clustering. For correlation clustering, we design O(1)-approximation algorithms with the semi-streaming O[approximately](n) space in the graph streaming model and with O[approximately](n) time in the query model, where n is the number of "vertices" in the graph. Furthermore, for the truly-streaming polylog "n" space regime, we design algorithms that approximate the "optimal cost" of correlation clustering. We test the polylog "n"-space algorithms on various input data and find that the practical performances are better than the "worst-case" guarantees. For hierarchical clustering, we give a single-pass semi-streaming algorithm that achieves O(1)-approximation for Dasgupta's objective, and we prove the cost-space trade-off in the single-pass setting; and (3) In part III, we move to more practically-driven problems of differential privacy (DP) and weak-strong oracle learning. For the former problem, we consider the differentially private release of "range queries" on graphs--a problem with wide applications in networks--and we give optimal bounds for pure and approximate DP. For the latter problem, weak-strong oracle learning is motivated by an industry setting where information is obtained from a cheap but noisy source and an accurate but expensive source. We study (metric) k-clustering and MST in this setting and obtain nearly-optimal algorithms with strong experimental performances. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]