:PROPERTIES:
:ID: c4a0d60f-49d3-4185-8c5b-f8a5a10a2ccc
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#+title: thesis/introduction
#+filetags: :project: :knowledge: :introduction:

Chapter 1 of the BGU MSc thesis on ROLL. Written last, after Ch. 2–4 are stable.
Parent: [[id:6294e2be-6189-4473-b363-a1dd9a75fb9b][thesis]]

** Thesis Narrative (corrected 2026-08-29)

The thesis is about learning under *label noise and class imbalance*, solved via
direct AUC optimization. The hero method is ROLL-AoC. The surprise finding is
*implicit* noise robustness — not a design goal, but a structural consequence of
distributional score fitting.

** Guidelines

- Target length: 4–6 pages
- Write last — contributions list and roadmap must match what the thesis actually delivers
- Structure: Hook → Problem statement → Contributions → Roadmap
- Do NOT explain the method — introduction is a promise, not a delivery

** Structure

1. *Hook* (~1–2 paragraphs) — concrete scenario where noisy labels + imbalance combine badly.
   Good candidates from experiments: ChestX-ray14 (NLP-extracted labels, IR≈7.5:1),
   credit card fraud (IR≈577:1), CIFAR-10N (crowdworker noise, 40% worst-annotator).
   Make the reader feel the problem before naming it.

2. *Problem statement* (~1–2 paragraphs) — three interlocking failures:
   - Standard losses (BCE, focal) fail under imbalance (accuracy wrong metric) AND noise
     (mislabeled samples produce large isolated gradient outliers)
   - Noise-robust losses (GCE, MAE) stay per-sample — no AUC connection
   - AUC-optimizing methods (LibAUC) use pairwise surrogates that lose direct connection to the curve
   Gap: no single method simultaneously optimizes AUC, handles imbalance structurally, and is
   robust to label noise.

3. *Contributions* (bulleted list):
   - ROLL: general framework for differentiable ROC-based optimization via score distribution fitting
   - Three instantiations: Gaussian, Beta, KDE (KDE is primary)
   - ROLL-AoC: direct numerical AUC integration via 99 per-FPR evaluations — distinct from pairwise surrogates
   - Gradient balance property: updates invariant to class-size ratio
   - Gradient locality property: gradient mass concentrates near operating threshold
   - Empirical: *implicit* noise robustness — ROLL-AoC outperforms noise-designed losses (GCE, MAE)
     at 20% noise, consistent across tabular (KEEL), image (CIFAR-10N), medical imaging (ChestX-ray14)

4. *Roadmap* (~1 paragraph) — one sentence per chapter, matching final chapter titles exactly.

** Gotchas

- Roadmap must exactly match final chapter titles — write it last
- Don't use the inseparability / cascade-classifier tangent from the old draft; it dilutes the argument
- Don't frame as "operating point optimization" — the pivot is AUC + label noise
- The noise robustness is *implicit* (emergent), not a design objective — this is the surprising result to sell