AUC: the probability view (with derivation and figures)
The crux: AUC is the probability that a random positive outranks a random negative. ROC geometry, likelihood-ratio slopes, and invariances fall out of that.
Gabriel Dunin-Borkowski
I publish technical essays and analytical notes at the intersection of applied AI, econometrics, and quantitative risk.
Recent writing
From RUM to Gravity: Using Random Utility to Derive Migration Flows.
A compact derivation showing how a random utility model aggregates into a gravity-style migration equation with multilateral resistance.
Itô's Lemma - Quick n' Dirty
A compact derivation of Ito's lemma from a Taylor expansion of an Ito process, highlighting why the second-order term survives.
Complete ROC & AUC derivation
A step-by-step derivation of ROC and AUC from class-conditional score distributions, ending with the probability interpretation of AUC.