Model complexity gap drives three separation rates; LOO-CV is inconsistent
BlackHC · x · 2026-09-09
BlackHC discusses loss separation rates in model selection: with equal loss floors, models separate at three distinct rates, where Δλ is the model complexity delta.
- Final height: gap Δλ/N — LOO-CV is inconsistent (Shao 1993)
- Last-half tail: Δλ·log 2 — constant
- Total area: Δλ·log N — grows without bound
He argues that "best model" is incomplete until we specify which part of learning and deployment we value. The full post covers the exact identity, the flip-order result, the regimes behind crossings, plus a toy experiment and an interactive panel.
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