Data Splits and Leakage

Data leakage occurs when training, feature construction, selection, or evaluation uses information that would not legitimately be available for the target use, making results optimistic. High training accuracy alone is not leakage, and not every strong proxy is illegal information.

Define the Information Boundary

unit             prediction object
prediction_time  when the output must be made
horizon          how far ahead the target lies
available_info   information genuinely available and allowed then
label_time       when the label occurs, matures, and may be revised
split_key        entities, groups, and times that must not cross sets

Legitimacy is relative to the deployment information set $\mathcal{I}(t)$. A field existing in a database does not mean it existed at prediction time or is permitted for use.

Leakage Types

Type	Example	Distortion	Control
target/post-outcome	discharge billing predicts admission-time risk	feature follows outcome	audit event times and lineage
temporal	random time-series split or future revisions	training sees the future regime	forward split and data vintages
entity/group	one patient/device appears on both sides	identity or history is memorized	group, sometimes group+time split
duplicate	crops or template copies cross sets	test is not a new case	group near-duplicates before splitting
preprocessing	scaler, imputer, PCA, selection fit globally	test distribution changes transforms	fit inside every training fold
model selection	test repeatedly changes model/threshold	test becomes validation	lock test or obtain a new holdout
benchmark contamination	training contains questions and answers	measures reproduction	provenance, deduplication, source/time isolation

A deployment-available proxy may still be a shortcut, bias, or brittle correlate without being leakage. Use subgroup, intervention, and shift tests rather than relabeling every problem.

Split to Simulate Use

Deployment question	Preferred split	Does not answer
new independent same-regime cases	stratified random	temporal change or identity memory
new patients/users/devices	group	future policy change
future period	temporal forward	new institution
new institution/region	external/group holdout	every external environment
spatially dependent cases	blocked spatial	arbitrary unseen-region extrapolation

Stratification preserves label proportions; it does not prevent group, time, or duplicate overlap.

Pipeline Invariant

For training indices $I_{tr}$ and validation indices $I_{va}$, every learned transform $T_\eta$ should satisfy

$$\hat\eta=\operatorname{fit}(T,D_{I_{tr}}), \qquad X'_{va}=T_{\hat\eta}(X_{I_{va}}).$$

This includes scaling, imputation, vocabulary, PCA, feature selection, target encoding, oversampling, and learned augmentation. Cross-validation refits each transform per fold. Nested CV uses an outer loop for evaluation and an inner loop for selection; selecting features globally before CV still leaks.

Worked Example: 30-Day Readmission

The system must predict at discharge whether a patient returns within 30 days. A flawed design randomly splits visits, uses billing states completed after the 30-day window, selects codes on all data, and tunes thresholds against test AUC.

A stronger design freezes the prediction-time field list; groups by patient and holds out a later cohort; fits imputation, vocabulary, and selection on training only; chooses model and threshold on validation; runs test once with hospital/time/subgroup slices; and excludes examples whose 30-day labels have not matured.

A lower score may reveal that the old system relied on identity or future information rather than that the corrected system became worse.

Leakage Probes

• record event, ingestion, and revision time for every feature;
• train suspicious features alone and trace anomalous performance;
• remove identifiers and high-cardinality proxies;
• audit exact and near duplicates;
• run label-permutation controls;
• assert groups do not cross sets and transforms never fit on test;
• acquire a fresh holdout after repeated benchmark inspection.

Permutation tests do not find every leak: if a direct label-coded feature is permuted together with the label, their relation may remain. Combine controls with lineage.

Distinctions

Overfitting learns sample noise through a valid pipeline. Leakage crosses an information boundary. Distribution shift changes the deployment distribution. Confounding distorts a causal interpretation. All four can coexist.

prediction_time: explicit
label_horizon_and_maturity: explicit
unit_and_group_key: explicit
split_algorithm_and_seed: versioned
all_learned_transforms_fit_on_train_only: true
test_used_for_selection: false
duplicate_and_overlap_audit: complete
feature_availability_lineage: reviewed
known_residual_risks: listed

This note focuses on offline supervised prediction. Online experiments, RL, federated learning, and continual learning add intervention, feedback, and policy leakage.