Articles
Algorithmic Accountability in Small Data: Sample-Size-Induced Bias Within Classification Metrics
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025
Abstract: Evaluating machine learning models is crucial not only for determining their technical accuracy but also for assessing their potential societal implications. While the potential for low-sample-size bias in algorithms is well known, we demonstrate the significance of sample-size bias induced by combinatorics in classification metrics. This revelation challenges the efficacy of these metrics in assessing bias with high resolution, especially when comparing groups of disparate sizes, which frequently arise in social applications. We provide analyses of the bias that appears in several commonly applied metrics and propose a model-agnostic assessment and correction technique. Additionally, we analyze counts of undefined cases in metric calculations, which can lead to misleading evaluations if improperly handled. This work illuminates the previously unrecognized challenge of combinatorics and probability in standard evaluation practices and thereby advances approaches for performing fair and trustworthy classification methods.
Link to PaperFood Deserts and k-Means Clustering
SIAMURO, 2023
Abstract: Food deserts are regions where people lack access to healthy foods. In this article we use k-means clustering to cluster the food deserts in two Bay Area counties. The centroids (means) of these clusters are optimal locations for intervention sites (such as food pantries) since they minimize the distance that a person within a food desert cluster would need to travel to reach the resources they require. We present the results of both a standard and a weighted k-means clustering algorithm. The weighted algorithm takes into account the poverty levels in each food desert when determining the placement of a centroid. We find that this weighting can make significant changes to the proposed locations of intervention sites.
Link to PaperUnpublished Reports
Properties of the cone of polynomials of fixed degree that preserve nonnegative matrices
Published on arXiv, 2024
Abstract: As was detailed by Loewy and London in [Linear and Multilinear Algebra 6 (1978/79), no.~1, 83--90], the cone of polynomials that preserve the nonnegativity of matrices may play an important role in the solution to the nonnegative inverse eigenvalue problem. In this paper, we start by showing the cone generated by polynomials of degree greater than or equal to 2n that preserve nonnegative matrices of order n is non-polyhedral. Next, a question posed by Loewy in [Linear Algebra and its Applications, 676(2023), 267--276], about how negative the center term can be in a degree 2n polynomial is answered. We extend this to show that a polynomial that preserves nonnegative matrices of order n can have it's the largest term, in absolute value, be arbitrarily negative with the remaining coefficients being one. We conclude, by exploring properties of the measure of the cone when restricted to the unit sphere and by proving some initial bounds of that volume.
Link to Paper