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Paul Savala

Publications and source records attributed to Paul Savala.

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Jointly Predicting Courses and Grades Using a Transformer-Based Model

Existing predictive models in learning analytics often treat student academic history as a simple sequence, overlooking the concurrent nature of courses taken within a semester. This simplification can lead to inaccurate performance predictions, particularly for students with heavy or challenging course loads. This paper introduces a TRansformer for Academic Course-grade Estimation (TRACE) that addresses this limitation by jointly predicting both the set of courses a student will take and their corresponding grades for an upcoming semester. Our approach encodes courses on a per-semester basis to capture the effects of course concurrency and utilizes a novel loss function combining course-set prediction with grade prediction. We demonstrate that predicting courses taken in addition to the grades in those courses leads to significant improvements in prediction quality. Trained on ten years of institutional data, our joint prediction model reduces mean absolute error by nearly 50% compared to an identical architecture that predicts grades alone. The model also outperforms traditional LSTM-based sequential models, as well as graph neural network-based approaches, and offers natural ways to incorporate student attribute data. This work demonstrates the utility of modern neural architectures for creating interpretable models that can be adapted to new institutions via retraining and recalibration, as well as the importance of key techniques, such as predicting courses taken during training. We discuss how this model could be incorporated into early detection systems at institutions of higher education.

cs.AI

Assessing win strength in MLB win prediction models

In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this work by training a comprehensive set of machine learning models using a common dataset. In addition, we relate the win probabilities produced by these models to win strength as measured by score differential. In doing so we show that the most common machine learning models do indeed demonstrate a relationship between predicted win probability and the strength of the win. Finally, we analyze the results of using predicted win probabilities as a decision making mechanism on run-line betting. We demonstrate positive returns when utilizing appropriate betting strategies, and show that naive use of machine learning models for betting lead to significant loses.

cs.LG

Computing the Laplace eigenvalue and level of Maass cusp forms

Let $f$ be a primitive Maass cusp form for a congruence subgroup $Γ_0(D) \subset $ SL($2,\mathbb{Z}$) and $λ_f(n)$ its $n$-th Fourier coefficient. In this paper it is shown that with knowledge of only finitely many $λ_f(n)$ one can often solve for the level $D$, and in some cases, estimate the Laplace eigenvalue to arbitrarily high precision. This is done by analyzing the resonance and rapid decay of smoothly weighted sums of $λ_f(n)e(αn^β)$ for $X \leq n \leq 2X$ and any choice of $α\in \mathbb{R}$, and $β>0$. The methods include the Voronoi summation formula, asymptotic expansions of Bessel functions, weighted stationary phase, and computational software. These algorithms manifest the belief that the resonance and rapid decay nature uniquely characterizes the underlying cusp form. They also demonstrate that the Fourier coefficients of a cusp form contain all arithmetic information of the form.

math.NT