Efficient quadratic entropy with distance sketches

Abstract:We detail scalable methods for approximating the quadratic entropy $p^T d p$ for arbitrary distributions $p$ and common distances $d$ of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where $d$ is held constant while $p$ varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.

Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Computation (stat.CO)

arXiv:2610.11976 [stat.ML]

(or arXiv:2610.11976v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.11976 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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