Student pathways — trajectories spanning academic readiness, course selections, grades, and enrollment outcomes — are critical for understanding educational progress, particularly in community college systems where pathways are highly diverse. Restricted access to student records and a sparsity of coherent pathway data pose barriers to modeling and broader research engagement. This paper contributes a scalable and explainable framework for generating synthetic student pathway data, along with a Bayesian network structure learning approach adapted to the sparsity and temporal complexity of educational trajectories. We present a generative modeling approach that produces realistic synthetic student pathway data by learning a Bayesian network trained on longitudinal student records across multiple tables linked across time. Our model captures complex conditional dependencies across hundreds of variables while remaining interpretable: each parameter encodes transparent relationships that can be inspected or adjusted. We show that our method outperforms an independent sampler in reproducing marginal, conditional, and higher-order patterns in the real data. Our analysis shows that existing k-anonymity rules are infeasible for real or synthetic data, motivating a shift toward model-aware approaches for privacy considerations in student pathway data.

"Everything is bigger in Texas" and this includes the big data challenges of the state’s educational system. But just as big is the opportunity for digital twin technologies to improve decision-making in education, with potential to improve student outcomes. This paper formulates an Educational Digital Twin, a novel approach to understanding, modeling, and analyzing educational data to address the complexities inherent in student pathways. By "student pathways", we refer to the joint facets of student behavior—evolving dynamically over time and encompassing not only course enrollments but also behavioral and academic factors. Unlike traditional approaches that rely on static analyses of historical data, the Educational Digital Twin applies the digital twin paradigm to model these pathways as a living construct that dynamically evolves alongside the physical world. At the heart of the Educational Digital Twin is a knowledge graph that organizes data into a semantic structure. By employing graph-theoretic methods, we manipulate this structure to derive multi-granular insights that inform decision-making. Our evaluation demonstrates how the Educational Digital Twin not only facilitates the dynamic integration of new data but also scales efficiently to handle complex datasets covering millions of students across hundreds of demographic and academic dimensions.

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of mechanical and dynamical systems (reliability, probability of failure, stability, etc.). Our algorithm locates contours using information from multiple sources, which are available in the form of relatively inexpensive, biased, and possibly noisy approximations to the original function. Considering multiple information sources can lead to significant cost savings. We also introduce the concept of contour entropy, a formal measure of uncertainty about the location of the zero contour of a function approximated by a statistical surrogate model. Our algorithm locates contours efficiently by maximizing the reduction of contour entropy per unit cost.

We consider the task of optimizing an objective function subject to inequality constraints when both the objective and the constraints are expensive to evaluate. Bayesian optimization (BO) is a popular way to tackle optimization problems with expensive objective function evaluations, but has mostly been applied to unconstrained problems. Several BO approaches have been proposed to address expensive constraints but are limited to greedy strategies maximizing immediate reward. To address this limitation, we propose a lookahead approach that selects the next evaluation in order to maximize the long-term feasible reduction of the objective function. We present numerical experiments demonstrating the performance improvements of such a lookahead approach compared to several greedy BO algorithms, including constrained expected improvement (EIC) and predictive entropy search with constraint (PESC).

We consider the problem of optimizing an expensive objective function when a finite budget of total evaluations is prescribed. In that context, the optimal solution strategy for Bayesian optimization can be formulated as a dynamic programming instance. This results in a complex problem with uncountable, dimension-increasing state space and an uncountable control space. We show how to approximate the solution of this dynamic programming problem using rollout, and propose rollout heuristics specifically designed for the Bayesian optimization setting. We present numerical experiments showing that the resulting algorithm for optimization with a finite budget outperforms several popular Bayesian optimization algorithms.