AUC 一样，为什么前几条的命中结果不同？

"""Exact empirical binary ROC AUC, with ties grouped and half pair credit."""
import csv
import json
from fractions import Fraction as F
from pathlib import Path

ROOT = Path(__file__).resolve().parent
BASE = [
    {"id": "P1", "label": 1, "a": 7, "b": 6},
    {"id": "P2", "label": 1, "a": 4, "b": 5},
    {"id": "P3", "label": 1, "a": 3, "b": 3},
    {"id": "N1", "label": 0, "a": 6, "b": 7},
    {"id": "N2", "label": 0, "a": 5, "b": 4},
    {"id": "N3", "label": 0, "a": 2, "b": 2},
    {"id": "N4", "label": 0, "a": 1, "b": 1},
]
CASES = [
    {"id": "rank_a", "rows": [{"id": r["id"], "label": r["label"], "score": str(r["a"])} for r in BASE]},
    {"id": "rank_b", "rows": [{"id": r["id"], "label": r["label"], "score": str(r["b"])} for r in BASE]},
    {"id": "rank_a_rescaled", "rows": [{"id": r["id"], "label": r["label"], "score": str(2 * r["a"] + 7)} for r in BASE]},
    {"id": "mixed_ties", "rows": [
        {"id": "P1", "label": 1, "score": "2"}, {"id": "P2", "label": 1, "score": "1"},
        {"id": "N1", "label": 0, "score": "2"}, {"id": "N2", "label": 0, "score": "0"}]},
    {"id": "all_tied", "rows": [
        {"id": "P1", "label": 1, "score": "0"}, {"id": "P2", "label": 1, "score": "0"},
        {"id": "N1", "label": 0, "score": "0"}, {"id": "N2", "label": 0, "score": "0"}]},
]


def prepare(rows):
    if not rows or len({r["id"] for r in rows}) != len(rows):
        raise ValueError("nonempty unique IDs required")
    if any(type(r["label"]) is not int or r["label"] not in (0, 1) for r in rows):
        raise ValueError("binary labels 0/1 required")
    if {r["label"] for r in rows} != {0, 1}:
        raise ValueError("ROC AUC undefined without both classes")
    return [{**r, "score": F(r["score"])} for r in rows]


def analyze(case):
    rows = prepare(case["rows"])
    positives = [r for r in rows if r["label"] == 1]
    negatives = [r for r in rows if r["label"] == 0]
    pairs = []
    for pos in positives:
        for neg in negatives:
            credit = F(1) if pos["score"] > neg["score"] else F(1, 2) if pos["score"] == neg["score"] else F(0)
            pairs.append({"case": case["id"], "positive_id": pos["id"], "negative_id": neg["id"],
                          "positive_score": str(pos["score"]), "negative_score": str(neg["score"]),
                          "credit": str(credit)})
    pair_auc = sum(F(row["credit"]) for row in pairs) / len(pairs)
    points = [{"case": case["id"], "threshold": "+infinity", "tp": 0, "fp": 0,
               "tpr": "0", "fpr": "0", "area_from_previous": "0"}]
    old_x, old_y, area = F(0), F(0), F(0)
    for threshold in sorted({r["score"] for r in rows}, reverse=True):
        selected = [r for r in rows if r["score"] >= threshold]
        tp = sum(r["label"] for r in selected)
        fp = len(selected) - tp
        x, y = F(fp, len(negatives)), F(tp, len(positives))
        piece = (x - old_x) * (y + old_y) / 2
        area += piece
        points.append({"case": case["id"], "threshold": str(threshold), "tp": tp, "fp": fp,
                       "tpr": str(y), "fpr": str(x), "area_from_previous": str(piece)})
        old_x, old_y = x, y
    assert (old_x, old_y) == (1, 1) and area == pair_auc
    ranking, found = [], 0
    for k, row in enumerate(sorted(rows, key=lambda r: (-r["score"], r["id"])), 1):
        found += row["label"]
        ranking.append({"case": case["id"], "rank": k, "id": row["id"], "label": row["label"],
                        "score": str(row["score"]), "positives_in_prefix": found, "precision_at_k": str(F(found, k))})
    summary = {"case": case["id"], "positive_count": len(positives), "negative_count": len(negatives),
               "pair_count": len(pairs), "pair_auc": str(pair_auc), "roc_auc": str(area),
               "precision_at_1": ranking[0]["precision_at_k"], "precision_at_3": ranking[2]["precision_at_k"],
               "ranking": [r["id"] for r in ranking]}
    return summary, pairs, points, ranking


def write_csv(name, rows):
    with (ROOT / name).open("w", encoding="utf-8", newline="") as handle:
        writer = csv.DictWriter(handle, fieldnames=list(rows[0]))
        writer.writeheader()
        writer.writerows(rows)


def main():
    summaries, pair_rows, roc_rows, rank_rows = [], [], [], []
    for case in CASES:
        summary, pairs, points, ranking = analyze(case)
        summaries.append(summary)
        pair_rows.extend(pairs)
        roc_rows.extend(points)
        rank_rows.extend(ranking)
    assert [s["pair_auc"] for s in summaries] == ["2/3", "2/3", "2/3", "5/8", "1/2"]
    assert [s["precision_at_1"] for s in summaries[:2]] == ["1", "0"]
    assert [s["precision_at_3"] for s in summaries[:2]] == ["1/3", "2/3"]
    assert summaries[0]["ranking"] == summaries[2]["ranking"]
    rejected = []
    for name, rows in [("empty", []), ("no_negative", [{"id": "x", "label": 1, "score": "1"}]),
                       ("no_positive", [{"id": "x", "label": 0, "score": "1"}]),
                       ("duplicate_id", [{"id": "x", "label": 0, "score": "0"}, {"id": "x", "label": 1, "score": "1"}])]:
        try:
            prepare(rows)
        except ValueError:
            rejected.append(name)
        else:
            raise AssertionError(name)
    inputs = {"positive_label": 1, "higher_is_more_positive": True, "sample_weights": "equal",
              "top_k_ties": "ID ascending within equal scores", "roc_ties": "entire score group moves together",
              "cases": CASES}
    report = {"scope": "Fabricated binary labels/scores; exact empirical ranking metrics, no trained classifier",
              "cases": summaries, "pair_rows": len(pair_rows), "roc_rows": len(roc_rows),
              "ranking_rows": len(rank_rows), "rejected_inputs": rejected}
    (ROOT / "auc-inputs.json").write_text(json.dumps(inputs, indent=2) + "\n", encoding="utf-8")
    (ROOT / "auc-report.json").write_text(json.dumps(report, indent=2) + "\n", encoding="utf-8")
    write_csv("auc-pairs.csv", pair_rows)
    write_csv("auc-roc.csv", roc_rows)
    write_csv("auc-rankings.csv", rank_rows)
    print(f"PASS auc_pairs: {len(CASES)} cases, {len(pair_rows)} pairs, {len(roc_rows)} ROC points, {len(rank_rows)} ranking rows")


if __name__ == "__main__":
    main()