#!/usr/bin/env python3
"""Choose a decision threshold for an imbalanced binary classifier, and undo resampling bias.
From a CSV of y_true (0/1) and y_score it evaluates every distinct score as a threshold and reports the
best one under each policy:
f-beta maximise F-beta (--beta, default 1; 2 = recall twice as important)
precision highest recall with precision >= --min-precision
recall highest precision with recall >= --min-recall
capacity flag exactly the top --k rows (review / call capacity)
cost minimise FP * --cost-fp + FN * --cost-fn per row
youden maximise TPR - FPR
For each: threshold, precision, recall, F1, flagged share, FP and FN counts.
Prior-shift correction: if the model was trained on resampled or reweighted data with positive
rate --train-rate, but the real positive rate is --true-rate, probabilities are biased. With both
flags the scores are corrected with
p' = p*a / (p*a + (1-p)*b), a = true/train, b = (1-true)/(1-train)
before thresholding, and expected calibration error (ECE) is shown before and after. --write FILE
saves the corrected scores.
Threshold choice on the evaluation set is optimistic: choose on validation data, report on test data.
Usage:
python threshold_tuner.py preds.csv --beta 2 --min-precision 0.5 --k 50 --cost-fp 8 --cost-fn 600
python threshold_tuner.py preds.csv --train-rate 0.5 --true-rate 0.02 --write corrected.csv
python threshold_tuner.py preds.csv --true-col label --score-col p --json
Exit codes: 0 done, 2 usage or data error.
"""
import argparse
import csv
import json
import sys
from collections import defaultdict
def sweep(scores, y):
"""Yield (threshold, tp, fp, fn, tn) for every distinct score, flagging score >= threshold."""
n, pos = len(y), sum(y)
groups = defaultdict(lambda: [0, 0])
for s, t in zip(scores, y):
groups[s][0] += t
groups[s][1] += 1
tp = flagged = 0
for s in sorted(groups, reverse=True):
h, c = groups[s]
tp += h
flagged += c
fp = flagged - tp
yield s, tp, fp, pos - tp, n - pos - fp
def row(thr, tp, fp, fn, tn, n):
p = tp / (tp + fp) if tp + fp else 0.0
r = tp / (tp + fn) if tp + fn else 0.0
return {"threshold": thr, "precision": p, "recall": r, "f1": 2 * p * r / (p + r) if p + r else 0.0,
"flagged_share": (tp + fp) / n, "tp": tp, "fp": fp, "fn": fn, "tn": tn}
def ece(scores, y, bins=10):
agg = defaultdict(lambda: [0.0, 0.0, 0])
for s, t in zip(scores, y):
b = agg[min(bins - 1, int(s * bins))]
b[0] += s
b[1] += t
b[2] += 1
return sum(abs(sp - st) for sp, st, _ in agg.values()) / len(y)
def main():
ap = argparse.ArgumentParser(description="Pick thresholds for imbalanced classifiers; correct prior shift.",
epilog=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
ap.add_argument("csv")
ap.add_argument("--true-col", default="y_true")
ap.add_argument("--score-col", default="y_score")
ap.add_argument("--beta", type=float, default=1.0)
ap.add_argument("--min-precision", type=float)
ap.add_argument("--min-recall", type=float)
ap.add_argument("--k", type=int)
ap.add_argument("--cost-fp", type=float)
ap.add_argument("--cost-fn", type=float)
ap.add_argument("--train-rate", type=float, help="positive rate the model was trained on (after resampling)")
ap.add_argument("--true-rate", type=float, help="real positive rate in production")
ap.add_argument("--write", help="write corrected scores to this CSV (needs --train-rate and --true-rate)")
ap.add_argument("--json", action="store_true")
a = ap.parse_args()
try:
with (sys.stdin if a.csv == "-" else open(a.csv, newline="", encoding="utf-8-sig")) as fh:
rd = csv.DictReader(fh)
if a.true_col not in (rd.fieldnames or []) or a.score_col not in (rd.fieldnames or []):
raise ValueError(f"need columns {a.true_col!r} and {a.score_col!r}")
rows = list(rd)
y = [int(float(r[a.true_col])) for r in rows]
s = [float(r[a.score_col]) for r in rows]
except (OSError, ValueError) as e:
print(f"error: {e}", file=sys.stderr)
return 2
if set(y) - {0, 1} or sum(y) in (0, len(y)):
print("error: y_true must be 0/1 with both classes present", file=sys.stderr)
return 2
out = {"rows": len(y), "positives": sum(y), "prevalence": sum(y) / len(y)}
if (a.train_rate is None) != (a.true_rate is None):
print("error: give both --train-rate and --true-rate", file=sys.stderr)
return 2
if a.train_rate is not None:
if not (0 < a.train_rate < 1 and 0 < a.true_rate < 1):
print("error: rates must be in (0, 1)", file=sys.stderr)
return 2
ca, cb = a.true_rate / a.train_rate, (1 - a.true_rate) / (1 - a.train_rate)
before = ece(s, y)
s = [p * ca / (p * ca + (1 - p) * cb) for p in s]
out["prior_correction"] = {"train_rate": a.train_rate, "true_rate": a.true_rate, "ece_before": before,
"ece_after": ece(s, y), "mean_score_after": sum(s) / len(s)}
if a.write:
with open(a.write, "w", newline="", encoding="utf-8") as f:
w = csv.writer(f)
w.writerow([a.true_col, a.score_col])
w.writerows([[t, round(p, 6)] for t, p in zip(y, s)])
n = len(y)
curve = [row(thr, tp, fp, fn, tn, n) for thr, tp, fp, fn, tn in sweep(s, y)]
b2 = a.beta ** 2
best = {}
fb = lambda r: (1 + b2) * r["precision"] * r["recall"] / (b2 * r["precision"] + r["recall"]) if r["precision"] + r["recall"] else 0
best[f"f{a.beta:g}"] = max(curve, key=fb)
best["youden"] = max(curve, key=lambda r: r["recall"] - r["fp"] / max(1, r["fp"] + r["tn"]))
if a.min_precision is not None:
ok = [r for r in curve if r["precision"] >= a.min_precision]
best[f"precision>={a.min_precision:g}"] = max(ok, key=lambda r: r["recall"]) if ok else None
if a.min_recall is not None:
ok = [r for r in curve if r["recall"] >= a.min_recall]
best[f"recall>={a.min_recall:g}"] = max(ok, key=lambda r: r["precision"]) if ok else None
if a.k:
ranked = sorted(s, reverse=True)
thr = ranked[min(a.k, n) - 1]
best[f"top-{a.k}"] = next(r for r in curve if r["threshold"] <= thr) if any(r["threshold"] <= thr for r in curve) else None
if a.cost_fp is not None and a.cost_fn is not None:
cost = lambda r: (r["fp"] * a.cost_fp + r["fn"] * a.cost_fn) / n
flag_none = {"threshold": float("inf"), "tp": 0, "fp": 0, "fn": sum(y), "tn": n - sum(y), "precision": 0.0,
"recall": 0.0, "f1": 0.0, "flagged_share": 0.0}
r = min(curve + [flag_none], key=cost)
best["min-cost"] = {**r, "cost_per_row": cost(r)}
out["bayes_threshold_if_calibrated"] = a.cost_fp / (a.cost_fp + a.cost_fn)
out["policies"] = best
if a.json:
print(json.dumps(out, indent=2, default=float))
return 0
print(f"{n} rows, {out['positives']} positives (prevalence {out['prevalence']:.2%})")
if "prior_correction" in out:
pc = out["prior_correction"]
print(f"prior correction {pc['train_rate']:g} -> {pc['true_rate']:g}: ECE {pc['ece_before']:.4f} -> "
f"{pc['ece_after']:.4f}, mean score {pc['mean_score_after']:.4f}" + (f"; wrote {a.write}" if a.write else ""))
print(f"\n{'policy':<18} {'threshold':>9} {'precision':>9} {'recall':>7} {'F1':>6} {'flagged':>8} {'FP':>6} {'FN':>5}")
for name, r in best.items():
if r is None:
print(f"{name:<18} not reachable on this data")
continue
extra = f" cost/row {r['cost_per_row']:.4f}" if "cost_per_row" in r else ""
print(f"{name:<18} {r['threshold']:>9.4g} {r['precision']:>9.3f} {r['recall']:>7.3f} {r['f1']:>6.3f} "
f"{r['flagged_share']:>8.1%} {r['fp']:>6} {r['fn']:>5}{extra}")
if "bayes_threshold_if_calibrated" in out:
print(f"\nBayes-optimal threshold for calibrated probabilities: {out['bayes_threshold_if_calibrated']:.4f}")
print("Choose the threshold on validation data and report metrics on a separate test set.")
return 0
if __name__ == "__main__":
sys.exit(main())
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