Who pays late?

A collections team can call two hundred accounts a day. Which two hundred?

Every ledger with credit in it faces the same morning: more accounts in arrears than hands to chase them. The ladder in case 02 decided what to send and when; the arrears path in case 04 decided who must not be chased. What neither did is decide who to call first. That is a ranking problem, and ranking is where a model earns its place: not to replace judgement, but to put the two hundred most likely-to-slip, highest-exposure accounts at the top of the list before anyone picks up a phone.

Thirty thousand real accounts, six months of "how late, how much billed, how much paid", and whether the next payment was missed.

The UCI Default of Credit Card Clients dataset (Yeh & Lien, 2009): 30,000 credit-card accounts from a Taiwanese bank, April to September 2005. It is used here because it has exactly the shape of a receivables ageing history — monthly repayment status, bill and payment amounts — and a clean, real outcome. 22.1% of accounts missed the next payment.

Before any model: what would fool it, and what would fool us.

Three things had to be settled first. Undocumented codes — the education and marital fields contain values the codebook never defines; they were folded into "other" rather than dropped. Time order — every feature is built from the six months before the outcome month; nothing from the scored month leaks in. And the protocol — a stratified 80/20 hold-out set touched exactly once, with five-fold cross-validation on the training half for every comparison, so the reported numbers are not the numbers the model was tuned on.

# features built only from history known before the month being predicted (train.py)
pay = d[PAY].clip(lower=-1)                       # -2 (no spend) and -1 (paid in full) both mean "not late"
f["late_now"]     = pay["PAY_1"].clip(lower=0)
f["months_late"]  = (pay > 0).sum(axis=1)
w = np.array([6, 5, 4, 3, 2, 1])                  # the last month counts most
f["late_recency"] = (pay.clip(lower=0).values * w).sum(axis=1) / w.sum()
ratio = np.where(prev_bill > 0, paid / np.maximum(prev_bill, 1), 1.0)   # share of last bill actually paid
f["pay_ratio_mean"] = np.clip(ratio, 0, 2).mean(axis=1)

X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.2, stratify=y, random_state=42)
cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)   # every comparison happens inside the training half

Fifteen features, all of them things a collector would recognise. The recency-weighted lateness score does most of the work.

Gradient boosting beats a good logistic baseline by 2.6 AUC points. More importantly, its probabilities mean what they say.

Fairness — reported, not assumed

Sex and age are not features. The model is still checked against them on the held-out set, because a feature like "share of bill paid" can carry demographic signal indirectly. It scores each group about as well as the whole, and its mean score tracks each group's actual miss rate:

Describe an account. The exported model scores it here — same trees, same probabilities as the Python — and explains itself.

Then the economics: where to stop calling

A probability is not a decision. Rank accounts by probability × exposure, contact the top k%, and every contact costs something while only some would-have-missed accounts pay because you called. Move the two levers below; the model's job is to make the best k visible.