区间写着九成覆盖，为什么某一类样本一次也没包住？

"""Finite-rank conformal arithmetic with synthetic residuals; no model training."""
import json
import math
from fractions import Fraction
from pathlib import Path


def threshold(scores, alpha):
    if not scores or not 0 < alpha < 1:
        raise ValueError("nonempty scores and alpha strictly between zero and one required")
    if any(not math.isfinite(s) or s < 0 for s in scores):
        raise ValueError("finite nonnegative residuals required")
    # Fraction keeps the displayed decimal alpha exact at integer boundaries.
    a = Fraction(str(alpha))
    rank = math.ceil((len(scores)+1)*(1-a))
    return (sorted(scores)[rank-1] if rank <= len(scores) else math.inf), rank


def naive_threshold(scores, alpha):
    rank = math.ceil(len(scores)*(1-Fraction(str(alpha))))
    return sorted(scores)[rank-1]


def main():
    all_scores = list(range(1, 10))
    trials = []
    # Condition on nine distinct scores; each one is equally likely to be the test score.
    for index, test in enumerate(all_scores):
        calibration = all_scores[:index]+all_scores[index+1:]
        q, rank = threshold(calibration, 0.2)
        wrong_q = naive_threshold(calibration, 0.2)
        trials.append({"test_score": test, "q":q,"rank":rank,
                       "covered":test <= q,"naive_covered":test <= wrong_q})
    covered, naive_covered = sum(t["covered"] for t in trials), sum(t["naive_covered"] for t in trials)
    assert covered == 8 and naive_covered == 7
    print(f"nine possible held-out ranks: corrected={covered}/9 naive={naive_covered}/9")
    q, rank = threshold(list(range(1, 9)), 0.1)
    assert rank == 9 and math.isinf(q)
    print(f"n=8 alpha=0.1: required_rank={rank} threshold=infinity")
    tie_q, _ = threshold([5]*8, 0.2)
    assert tie_q == 5 and all(5 <= tie_q for _ in range(9))
    print("tied residuals: inclusive <= threshold covers 9/9")
    calibration = [1.0]*90+[10.0]*9
    group_q, group_rank = threshold(calibration, 0.1)
    groups = {"easy": [0.5]*90, "hard": [5.0]*10}
    coverage = {name:sum(s <= group_q for s in scores)/len(scores) for name,scores in groups.items()}
    pooled = sum(s <= group_q for scores in groups.values() for s in scores)/100
    shifted = sum(s <= group_q for s in [5.0]*100)/100
    assert group_q == 1 and group_rank == 90
    assert pooled == 0.9 and coverage == {"easy":1.0,"hard":0.0} and shifted == 0.0
    print(f"constructed groups: q={group_q:.1f} pooled={pooled:.1%} easy={coverage['easy']:.1%} hard={coverage['hard']:.1%}")
    print(f"all-hard shifted input: observed coverage={shifted:.1%}")
    invalid = 0
    for scores, alpha in [([], 0.1), ([1], 0), ([1], 1), ([-1], 0.1), ([math.nan], 0.1)]:
        try:
            threshold(scores, alpha)
        except ValueError:
            invalid += 1
    assert invalid == 5
    print("checks=11 passed; ranks and constructed residuals only")
    Path("report.json").write_text(json.dumps({"rank_trials":trials,"rank_corrected_hits":covered,
        "naive_hits":naive_covered,"unbounded_case":{"n":8,"alpha":0.1,"rank":9,"q":"infinity"},
        "group_threshold":group_q,"group_coverage":coverage,"pooled_coverage":pooled,
        "shifted_coverage":shifted,"checks":11}, indent=2, allow_nan=False), encoding="utf-8")


if __name__ == "__main__":
    main()