CJE — Causal Judge Evaluation

LLM-judge scores are cheap, plentiful, and miscalibrated. In our benchmark, naive 95% confidence intervals built on raw judge scores contained the true value 0% of the time. CJE calibrates your judge against a small slice of ground truth (5–25% of samples), evaluates your policies at scale, and reports uncertainty you can defend — including telling you when not to trust the result.

60 seconds

pip install cje-eval

Generate responses from each candidate policy on a shared prompt set, judge everything, and attach ground-truth labels (oracle_label) to the slice you can afford — human raters, expert review, a downstream KPI. Any bounded scale works (0–1, 0–100, Likert). CJE needs at least 10 labeled rows pooled across policies — they can all come from one policy, and even that policy doesn't need labels on every row:

from cje import analyze_dataset

# One policy carries the oracle slice — CJE learns the judge→oracle mapping
# once and applies it to every unlabeled response, in any policy. Coverage
# is never required to be complete: gpt-5.6 has 20 responses with labels on
# only 10 (oracle_label=None means unlabeled); fable-5 has no labels at all.
labeled = [(0.62, 0.55), (0.68, 0.60), (0.72, 0.70), (0.76, 0.74), (0.79, 0.75),
           (0.83, 0.80), (0.85, 0.90), (0.88, 0.92), (0.91, 0.88), (0.95, 0.97)]
unlabeled = [0.64, 0.69, 0.73, 0.77, 0.80, 0.84, 0.87, 0.89, 0.92, 0.94]
judge_only = [0.70, 0.74, 0.75, 0.78, 0.81, 0.83, 0.86, 0.90, 0.93, 0.94]

results = analyze_dataset(
    fresh_draws_data={
        "gpt-5.6": [
            {"prompt_id": f"q{i:02d}", "judge_score": s, "oracle_label": y}
            for i, (s, y) in enumerate(labeled + [(u, None) for u in unlabeled])
        ],
        "fable-5": [
            {"prompt_id": f"q{i:02d}", "judge_score": s}
            for i, s in enumerate(judge_only)
        ],
    }
)

for policy, estimate, (lo, hi) in zip(
    results.metadata["target_policies"], results.estimates, results.ci()
):
    print(f"{policy:15s} {estimate:.3f}  95% CI [{lo:.3f}, {hi:.3f}]")

fable-5         0.811  95% CI [0.751, 0.873]
gpt-5.6         0.784  95% CI [0.589, 0.844]

fable-5 gets a calibrated estimate and an honest CI without a single label of its own, and gpt-5.6's ten unlabeled rows are covered by the same transfer — labels are a pooled budget, not a per-row requirement. That transfer is what the labels-under-every-policy workflow wastes money re-buying.

And when the data can't support an answer, CJE says so instead of handing you a confident number. Here a candidate policy's judge scores land mostly outside the range where the calibrator saw oracle labels — the run emits the paper's coverage badge and refuses level claims for that policy:

REFUSE-LEVEL for policy 'candidate': 88.3% of fresh-draw judge scores fall
outside the oracle calibration range [0.161, 0.595]. Do not ship level
(absolute) claims for this policy; rankings may stand. Collect oracle labels
covering the missing score range.

The cje analyze CLI takes the same gates into account before crowning a winner:

⚠️ Best by point estimate: candidate (UNRELIABLE — see diagnostics)
🏆 Best reliable policy: baseline

→ Runnable Colab with real data · Full docs

Is CJE the right tool?

How it works

1. Calibrate: learn the judge → oracle mapping on the labeled slice (isotonic, two-stage when needed; mean-preserving by construction; cross-fitted).
2. Evaluate: score every policy's fresh responses through the calibrated judge and compare policies on the same prompts.
3. Audit & refuse: a transport audit per policy (does the calibration still hold on this policy's outputs?) and a coverage badge for level claims (were there oracle labels where this policy's scores live?). Failing gates change the output — they are not footnotes.

Confidence intervals account for the judge being learned from a finite label budget (calibration-aware inference), not just sampling noise.

Calibrated estimates with 95% CIs (valid under the calibration and transport checks CJE runs by default)

Validation on real ground truth

• HealthBench (physician labels, n=29,511): two LLM judges were overconfident by 24.5 and 13.0 points and disagreed with each other by up to 73 points on specific criteria categories. Calibrated on 5% physician labels (~1,400 records), both converged to the physician ground truth. Read the full audit →
• Chatbot Arena (4,961 prompts, 5 policies): 99% pairwise ranking accuracy at a 5% oracle fraction — 14× cheaper than labeling everything, with ~95% CI coverage vs 0% for naive judge-score CIs. An adversarial policy that fools the judge is correctly flagged by the transport audit. Paper →

The array API

calibrated_mean_ci is the library's bottom layer — a ppi_py-style primitive that takes plain numpy arrays and returns a calibrated mean with an honest CI. Use it when you have one sample of judge scores and a partial oracle slice; use analyze_dataset for multi-policy comparisons.

import numpy as np
from cje import calibrated_mean_ci

rng = np.random.default_rng(0)
scores = rng.uniform(size=400)                      # judge scores for every sample
labels = np.full(400, np.nan)                       # NaN = unlabeled
labeled = rng.choice(400, size=100, replace=False)  # oracle slice (25%)
labels[labeled] = np.clip(scores[labeled] + rng.normal(0, 0.1, size=100), 0, 1)

result = calibrated_mean_ci(scores, labels)
print(result.summary())

Calibrated mean: 0.5316 (SE 0.0175, CI [0.4965, 0.5649], n=400, n_oracle=100, bootstrap)

result.calibrator is reusable: transport_audit(probe_scores, probe_labels, result.calibrator) checks whether the calibration still holds on a new slice. result.diagnostics["boundary_card"] carries the coverage badge.

Documentation

Bridges: Already running evals in Promptfoo, TruLens, LangSmith, or OpenCompass? Convert those outputs into CJE format with one command.

Module deep dives: Calibration · Diagnostics · Estimators · Interface/API · Data formats

Use CJE from your AI agent

skills/cje/ is an Agent Skill that teaches Claude Code and similar agents to run CJE correctly — reshape your data, drive the labeling loop, calibrate, compare, and respect the refusal gates — instead of averaging raw judge scores.

• Claude Code (all projects): mkdir -p ~/.claude/skills/cje && curl -fsSL https://raw.githubusercontent.com/cimo-labs/cje/main/skills/cje/SKILL.md -o ~/.claude/skills/cje/SKILL.md && curl -fsSL https://raw.githubusercontent.com/cimo-labs/cje/main/skills/cje/reference.md -o ~/.claude/skills/cje/reference.md
• Project-level: cp -r skills/cje .claude/skills/ from a checkout of this repo.
• Other agents: point your agent at skills/cje/SKILL.md — plain Markdown; reference.md loads on demand.

Notes on 0.4.0

0.4.0 is a breaking release: CJE is now Direct-mode only. The off-policy machinery — importance-sampling and doubly-robust estimators (calibrated-ips, dr-cpo, mrdr, tmle, stacked-dr), teacher forcing, SIMCal weight stabilization, and the overlap diagnostics — has been removed. Our own paper's results drove the cut: for realistic LLM policy pairs, importance weighting failed even when ESS looked healthy (target-typicality coverage 0.19–0.49, far below the 0.70 gate), and the best DR stack merely matched Direct mode's accuracy at ~12× the compute. Direct mode — fresh draws, calibrated judge, audits — is what the evidence supports, so it is now the whole product.

• Need IPS/DR from logged propensities? Pin the frozen OPE line: pip install "cje-eval==0.3.*" (maintained on the 0.3.x branch; docs at the v0.3.0 tag; requires Python <=3.12 — on 3.13 use a 3.12 env for OPE).
• Have old logged data with judge_score + oracle_label? It still works as the calibration source: analyze_dataset(fresh_draws_dir=..., calibration_data_path="logged.jsonl").
• Removed entry points raise migration errors that say exactly this.

Full details in the CHANGELOG.

Development

git clone https://github.com/cimo-labs/cje.git
cd cje && poetry install && make test

Citation

If you use CJE in your research, please cite:

@misc{landesberg2025causaljudgeevaluationcalibrated,
  title={Causal Judge Evaluation: Calibrated Surrogate Metrics for LLM Systems},
  author={Eddie Landesberg},
  year={2025},
  eprint={2512.11150},
  archivePrefix={arXiv},
  primaryClass={stat.ME},
  url={https://arxiv.org/abs/2512.11150},
}

License

MIT — See LICENSE for details.