Stieltjes integrals power diagnostic AI: modeling how classifier AUC scales with training samples
PTenigma · x · 2026-10-25
- The author uses Stieltjes integrals in diagnostic AI to model how a classifier's AUC changes with the number N of training samples.
- The integrator is a spectral distribution derived from the data's Gram matrix, weighted by how strongly disease-related signal loads on each eigenvector.
- The attached figure gives an intuitive explainer: treat the integrator g as a clock that can speed up, slow down, or jump, unifying sums and integrals in one framework.
- Historical tidbit: Stieltjes introduced his integral in 1894, the year he died at 38, in work on continued fractions—well before Lebesgue and Radon extended these ideas.
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