#!/usr/bin/env python3
"""Diagnose a regression target and recommend the loss, transform and model family that fit its shape.
Reads one numeric column and reports: quantiles, mean vs median, skew, tail ratio (p99 / median),
share of zeros, negatives, integer-ness, bounded [0, 1] proportions, and robust outliers. Then
recommends one of:
squared error symmetric, light tails
absolute / Huber heavy-tailed noise or outliers you do not want to chase
log1p target positive, right-skewed, multiplicative effects (predicts the median-ish)
Gamma strictly positive, skewed, variance grows with the mean^2 (claim size)
Poisson counts, variance ~ mean
Tweedie (1 < p < 2) many exact zeros plus a positive skewed tail (insurance loss, spend)
(two-part / hurdle) suggested alongside Tweedie when zeros exceed half the rows, and for
counts with far more zeros than a Poisson with the same mean would give
logit / beta proportions in (0, 1)
quantile (pinball) when the business needs a percentile, not the mean
and the matching objective names for scikit-learn, LightGBM, XGBoost and CatBoost.
Usage:
python target_diagnostics.py data.csv --target price
python target_diagnostics.py data.csv --target claim_amount --need-quantile 0.9
python target_diagnostics.py data.csv --target spend_90d --json
Exit codes: 0 diagnosed, 2 usage error or non-numeric target.
"""
import argparse
import csv
import json
import math
import sys
MISSING = {"", "na", "n/a", "nan", "null", "none", "?"}
def q(xs, p):
pos = (len(xs) - 1) * p
lo, hi = math.floor(pos), math.ceil(pos)
return xs[lo] + (xs[hi] - xs[lo]) * (pos - lo)
def describe(xs):
xs = sorted(xs)
n = len(xs)
mean = sum(xs) / n
var = sum((x - mean) ** 2 for x in xs) / n
sd = math.sqrt(var)
med = q(xs, 0.5)
mad = q(sorted(abs(x - med) for x in xs), 0.5) * 1.4826
pos = [x for x in xs if x > 0]
logs = [math.log(x) for x in pos]
lmean = sum(logs) / len(logs) if logs else 0.0
lsd = math.sqrt(sum((l - lmean) ** 2 for l in logs) / len(logs)) if len(logs) > 1 else 0.0
return {
"n": n, "min": xs[0], "p01": q(xs, 0.01), "p25": q(xs, 0.25), "median": med, "mean": mean,
"p75": q(xs, 0.75), "p99": q(xs, 0.99), "max": xs[-1], "std": sd,
"skew": 0.0 if sd == 0 else sum(((x - mean) / sd) ** 3 for x in xs) / n,
"skew_of_log_positive": 0.0 if lsd == 0 else sum(((l - lmean) / lsd) ** 3 for l in logs) / len(logs),
"zero_share": sum(1 for x in xs if x == 0) / n, "negative_share": sum(1 for x in xs if x < 0) / n,
"integer": all(float(x).is_integer() for x in xs), "distinct": len(set(xs)),
"tail_ratio": (q(xs, 0.99) / med) if med > 0 else None,
"dispersion": var / mean if mean > 0 else None,
"outlier_share": sum(1 for x in xs if mad and abs(x - med) / mad > 5) / n,
}
OBJECTIVES = {
"squared": ("squared error", "HistGradientBoostingRegressor(loss='squared_error') / Ridge",
"objective='regression'", "objective='reg:squarederror'", "loss_function='RMSE'"),
"huber": ("Huber / absolute error", "HistGradientBoostingRegressor(loss='absolute_error') / HuberRegressor",
"objective='huber' (alpha=delta) or 'regression_l1'", "objective='reg:pseudohubererror' or 'reg:absoluteerror'",
"loss_function='Huber:delta=...' or 'MAE'"),
"log": ("log1p target + squared error", "TransformedTargetRegressor(func=np.log1p, inverse_func=np.expm1)",
"train on log1p(y), objective='regression'", "train on log1p(y)", "train on log1p(y) or loss_function='RMSE'"),
"gamma": ("Gamma deviance (log link)", "HistGradientBoostingRegressor(loss='gamma') / GammaRegressor",
"objective='gamma'", "objective='reg:gamma'", "loss_function='Tweedie:variance_power=1.99' (Gamma-like)"),
"poisson": ("Poisson deviance (log link)", "HistGradientBoostingRegressor(loss='poisson') / PoissonRegressor",
"objective='poisson'", "objective='count:poisson'", "loss_function='Poisson'"),
"tweedie": ("Tweedie deviance, power in (1, 2)", "TweedieRegressor(power=1.5, link='log') (HGB has no tweedie loss)",
"objective='tweedie', tweedie_variance_power=1.5", "objective='reg:tweedie', tweedie_variance_power=1.5",
"loss_function='Tweedie:variance_power=1.5'"),
"hurdle": ("two-part model: P(y > 0) classifier x E[y | y > 0] regressor", "classifier + regressor on positives",
"binary + gamma/regression on positives", "binary:logistic + reg:gamma on positives",
"Logloss + RMSE/Tweedie on positives"),
"logit": ("logit-transformed proportion or cross-entropy on [0,1] targets", "TransformedTargetRegressor(logit/expit)",
"objective='cross_entropy' (xentropy) with y in [0, 1]", "objective='reg:logistic' with y in [0, 1]",
"loss_function='CrossEntropy' (targets in [0,1]) or RMSE on logit"),
"quantile": ("quantile (pinball) loss", "HistGradientBoostingRegressor(loss='quantile', quantile=q)",
"objective='quantile', alpha=q", "objective='reg:quantileerror', quantile_alpha=q",
"loss_function='Quantile:alpha=q'"),
}
def recommend(d, need_q):
why = []
if need_q:
return "quantile", [f"the decision needs the {need_q:.0%} quantile (safety stock, upper bound), not the mean"]
if 0 <= d["min"] and d["max"] <= 1 and not d["integer"]:
return "logit", ["values lie in [0, 1]: a proportion; keep predictions inside the bounds"]
if d["integer"] and d["min"] >= 0 and d["distinct"] <= max(50, 0.2 * d["n"]):
disp = d["dispersion"]
why.append(f"non-negative integer counts (variance/mean {disp:.2f})" if disp else "non-negative counts")
p0 = math.exp(-d["mean"]) # zero share a Poisson with this mean would produce
if d["zero_share"] > p0 + 0.1:
why.append(f"zeros {d['zero_share']:.0%} vs {p0:.0%} expected under Poisson: zero-inflated; consider a "
"hurdle model or Tweedie, or check for a missing exposure offset")
elif disp and disp > 2:
why.append("over-dispersed: the Poisson mean is fine for ranking, but intervals need negative binomial / Tweedie")
return "poisson", why
if d["min"] >= 0 and d["zero_share"] > 0.05 and d["skew"] > 1:
why = [f"{d['zero_share']:.0%} exact zeros plus a right-skewed positive part (skew {d['skew']:.1f}): "
"compound Poisson-Gamma (Tweedie) models both in one loss"]
if d["zero_share"] > 0.5:
why.append("alternative: a two-part model (P(y > 0) x E[y | y > 0]) when zeros come from a different process")
return "tweedie", why
if d["min"] > 0 and d["skew"] > 1:
if abs(d["skew_of_log_positive"]) < 0.5:
return "log", [f"right-skewed (skew {d['skew']:.1f}) and roughly log-normal (skew of log "
f"{d['skew_of_log_positive']:.2f}): log1p target or Gamma loss"]
return "gamma", [f"strictly positive and right-skewed (skew {d['skew']:.1f}); log is not enough to symmetrise"]
if d["outlier_share"] > 0.01 or abs(d["skew"]) > 2:
return "huber", [f"{d['outlier_share']:.1%} extreme values / skew {d['skew']:.1f}: a robust loss stops them dominating"]
return "squared", ["roughly symmetric with light tails: squared error estimates the mean well"]
def main():
ap = argparse.ArgumentParser(description="Recommend loss / transform for a regression target.", epilog=__doc__,
formatter_class=argparse.RawDescriptionHelpFormatter)
ap.add_argument("csv")
ap.add_argument("--target", required=True)
ap.add_argument("--need-quantile", type=float, help="the decision needs this quantile (0-1), e.g. 0.9")
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:
reader = csv.DictReader(fh)
if a.target not in (reader.fieldnames or []):
raise ValueError(f"target {a.target!r} not found")
raw = [(r[a.target] or "").strip() for r in reader]
xs = [float(v) for v in raw if v.lower() not in MISSING]
except (OSError, ValueError) as e:
print(f"error: {e}", file=sys.stderr)
return 2
if len(xs) < 10:
print("error: fewer than 10 numeric target values", file=sys.stderr)
return 2
d = describe(xs)
d["missing"] = len(raw) - len(xs)
choice, why = recommend(d, a.need_quantile)
name, sk, lgb, xgb, cb = OBJECTIVES[choice]
notes = []
if choice == "log":
notes.append("log-target predictions estimate the conditional median; for totals multiply by a smearing "
"factor mean(exp(residuals)) or use the Gamma/Tweedie objective")
if d["tail_ratio"] and d["tail_ratio"] > 10:
notes.append(f"p99 is {d['tail_ratio']:.0f}x the median: report errors by segment; RMSE will be dominated by the tail")
if d["negative_share"] > 0 and choice in ("squared", "huber"):
notes.append("negative values present: log, Gamma, Poisson and Tweedie are not applicable")
if d["missing"]:
notes.append(f"{d['missing']} rows without a target: check why before dropping them")
metric = {"squared": "RMSE (+MAE)", "huber": "MAE (+RMSE)", "log": "MAE / WAPE in original units, RMSLE",
"gamma": "mean Gamma deviance, MAE", "poisson": "mean Poisson deviance, MAE", "tweedie": "mean Tweedie deviance, MAE",
"hurdle": "MAE, plus AUC of the zero/non-zero part", "logit": "MAE, cross-entropy", "quantile": "pinball loss at q, coverage"}[choice]
out = {"target": a.target, "stats": {k: (round(v, 6) if isinstance(v, float) else v) for k, v in d.items()},
"recommendation": choice, "loss": name, "why": why, "sklearn": sk, "lightgbm": lgb, "xgboost": xgb,
"catboost": cb, "metric": metric, "notes": notes}
if a.json:
print(json.dumps(out, indent=2))
return 0
s = out["stats"]
print(f"Target {a.target!r}: n={s['n']} min={s['min']:g} median={s['median']:g} mean={s['mean']:g} "
f"p99={s['p99']:g} max={s['max']:g}")
print(f" skew {s['skew']:.2f} (of log: {s['skew_of_log_positive']:.2f}) zeros {s['zero_share']:.1%} "
f"negatives {s['negative_share']:.1%} integer {s['integer']} outliers {s['outlier_share']:.1%}")
print(f"\nRECOMMENDED: {name}")
for w in why:
print(f" why: {w}")
print(f" scikit-learn: {sk}\n LightGBM: {lgb}\n XGBoost: {xgb}\n CatBoost: {cb}\n metric: {metric}")
for n_ in notes:
print(f" note: {n_}")
return 0
if __name__ == "__main__":
sys.exit(main())
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