backup: 2026-08-29 06:59

thesismethod.org

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 #+title: thesis/method
 #+filetags: :project: :knowledge: :method:
 
-:PROPERTIES:
-:ID: thesis-method
-:END:
-
-#+title: thesis/method
-#+filetags: :project: :knowledge: :method:
-
 Chapter 3 of the BGU MSc thesis on ROLL. Core contribution chapter. Currently ~30 pages.
 Parent: [[id:6294e2be-6189-4473-b363-a1dd9a75fb9b][thesis]]
 
+** How roll-aoc Works (CRITICAL — post-pivot hero method)
+
+=roll-aoc= optimizes full AUC by:
+1. Sampling 100 evenly-spaced FPR points across [0, 1]
+2. Computing ROLL's TPR estimate at each point
+3. Averaging — this is a Monte Carlo approximation of the AUC integral
+
+This is *not* partial AUC (which integrates over a sub-range).
+This is *not* the pairwise ranking formulation (LibAUC/compositional AUC).
+It is a direct numerical integration of the ROC curve via 100 ROLL evaluations.
+
+This distinction must be stated clearly in Ch. 3 and Ch. 2 related work.
+
 ** Guidelines
 
 - sec:problem-formulation is now notation-only — motivation deferred to Ch. 2
@@ -48,4 +54,4 @@ Parent: [[id:6294e2be-6189-4473-b363-a1dd9a75fb9b][thesis]]
   σ'(τ − x_i) / Σ_j σ'(τ − x_j) where sum is over ALL of B_0 — sympy-verified
 - Beta ROLL: translation-invariance does NOT hold when scores pass through sigmoid before fitting;
   gradient-balance property breaks for Beta — documented in sec:roll-properties
-- Gradient-balance proof uses a uniform-shift argument; requires translation-invariant CDF estimator
+- Gradient-balance proof uses a uniform-shift argument; requires translation-invariant CDF estimator