58 lines
2.8 KiB
Org Mode
58 lines
2.8 KiB
Org Mode
:PROPERTIES:
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:ID: 0543ac39-af9b-40fd-9973-e60576a20695
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:END:
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#+title: thesis/method
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#+filetags: :project: :knowledge: :method:
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Chapter 3 of the BGU MSc thesis on ROLL. Core contribution chapter. Currently ~30 pages.
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Parent: [[id:6294e2be-6189-4473-b363-a1dd9a75fb9b][thesis]]
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** How roll-aoc Works (CRITICAL — post-pivot hero method)
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=roll-aoc= optimizes full AUC by:
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1. Sampling 100 evenly-spaced FPR points across [0, 1]
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2. Computing ROLL's TPR estimate at each point
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3. Averaging — this is a Monte Carlo approximation of the AUC integral
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This is *not* partial AUC (which integrates over a sub-range).
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This is *not* the pairwise ranking formulation (LibAUC/compositional AUC).
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It is a direct numerical integration of the ROC curve via 100 ROLL evaluations.
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This distinction must be stated clearly in Ch. 3 and Ch. 2 related work.
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** Guidelines
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- sec:problem-formulation is now notation-only — motivation deferred to Ch. 2
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via \Cref{sec:imbalanced-tpr-fpr,sec:neyman-pearson}
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- sec:imbalanced-tpr-fpr and sec:neyman-pearson were removed from this chapter and live in Ch. 2
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- Both objectives (TPR@FPR and FPR@TPR) are equivalent by negating scores and swapping labels;
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all derivations given for TPR@FPR only — FPR@TPR follows by transformation
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** Section Structure
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| Section | Label | Status |
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|---------|-------|--------|
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| Problem Formulation (notation only) | sec:problem-formulation | Done |
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| The ROLL Framework | sec:roll-framework | Written |
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| Differentiability Problem | sec:differentiability-problem | Written |
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| Score Distribution Fitting | sec:score-distribution-fitting | Written |
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| General ROLL Formulation and Derivation | sec:roll-formulation | Written — core theoretical contribution |
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| Gaussian ROLL (forward + gradient) | sec:roll-gaussian | Written |
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| Beta ROLL (forward + gradient) | sec:roll-beta | Stub — TBD |
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| KDE ROLL (forward + gradient) | sec:roll-kde | Written |
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| Properties | sec:roll-properties | Written — gradient balance + locality |
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| Custom Backward Pass | sec:roll-backward | Stub — TBD |
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| Numerical Stability | sec:roll-numerical-stability | Stub — TBD |
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| Bandwidth Estimation (ISJ + scheduling) | sec:kde-bandwidth | Written |
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** Gotchas
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- KDE backward pass uses inverse-function-theorem approach deliberately; implicit differentiation
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was considered and rejected — user needs to explain the derivation in their own words
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- Correct gradient of threshold w.r.t. negative-class score:
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σ'(τ − x_i) / Σ_j σ'(τ − x_j) where sum is over ALL of B_0 — sympy-verified
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- Beta ROLL: translation-invariance does NOT hold when scores pass through sigmoid before fitting;
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gradient-balance property breaks for Beta — documented in sec:roll-properties
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- Gradient-balance proof uses a uniform-shift argument; requires translation-invariant CDF estimator
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