Calibration Error Estimation

calibration-error-estimation

The Verification Tax: Fundamental Limits of AI Auditing in the Rare-Error Regime — Jason Z Wang (arXiv:2604.12951, 2026)

What this evaluates

Evaluates the sample complexity and verification cost required to estimate calibration error in AI models under rare-error regimes. It probes whether passive querying or active querying can reliably detect miscalibration and how estimation error scales with sample size and model smoothness.

Datasets

• Synthetic Calibration Gap — total ?; splits: test (-1)

Metrics

• estimation error (primary) — range: other
  • Absolute difference between the true calibration gap Δ(p) = A sin(2πkp) and the estimated gap, averaged over the probability space.

Input / output format

Input: Probability scores p sampled from Beta((1-ε)/ε, 1) and binary labels Y ~ Bern(p + Δ(p)).

Output: Estimated calibration gap or verification query decisions.

Scoring recipe

def compute_estimation_error(true_gap, estimated_gap):
    return abs(true_gap - estimated_gap)

# true_gap = A * sin(2 * pi * k * p)
# estimated_gap derived from passive/active querying on m samples

Common pitfalls

• Assuming self-evaluation without ground truth yields significant information.
• Overlooking the phase transition at m·ε ≈ 1 where miscalibration becomes fundamentally undetectable.

Evidence (verbatim from paper)

Figure 12: Synthetic slope study: estimation error versus sample size for increasing numbers of zero-crossings.

Citation

@misc{wang2026verificationtax,
  title={The Verification Tax: Fundamental Limits of AI Auditing in the Rare-Error Regime},
  author={Jason Z Wang},
  year={2026},
  note={arXiv:2604.12951}
}

• arXiv: 2604.12951