Proxy variables re-introduce excluded attributes into models

What it is

Proxy variables are features correlated with an excluded sensitive attribute that can stand in for it: postal codes for residential segregation, purchase histories for income and race, school names for class, writing style for language community. Once the sensitive attribute is banned, a model drawing predictive power from these proxies performs proxy discrimination — nominally not using the attribute while deciding by its shadow. What separates a proxy from mere unintentional redundancy is identifiability: a proxy is a single, nameable feature; redundancy is a diffuse combination.

Why it happens

Proxies gain predictive power along two pathways of different ethical character. First, the proxy's own signal is valid: spending stability genuinely predicts default; school quality genuinely predicts some ability — the model uses it for accuracy, and group disparity arrives as a by-product; such proxies resist simple bans because banning them costs prediction. Second, the proxy is a pure stand-in: unrelated to the target, its only contribution is marking the group — using it equals using the attribute itself. Most real proxies sit between the poles and shift with data scale: the more features and the finer the granularity (coordinates precise to buildings, transaction-by-transaction sequences), the stronger any proxy's group-marking ability. Commercial collection also manufactures proxies deliberately: spending-power tiers, lifestyle labels, interest clusters — productized intermediate variables that are commercialized aliases of sensitive attributes.

Studying it

Standard proxy audits train a sensitive-attribute predictor on allowed features, measuring single-feature and combined contributions (per-feature correlation, leave-one-out importance, SHAP-style attribution); high-contribution features are proxy candidates. A second test asks "which part of the proxy is useful": separate the component orthogonal to the sensitive attribute, retrain, and if predictive power drops sharply, the model was mostly using the group marker rather than the legitimate signal. Variables include proxy–attribute correlation strength, target nature, and feature granularity. Methodological cautions: attribution methods distribute contribution unstably across correlated features (two collinear proxies claim each other's credit), so conclusions rest on consistency across attribution methods; and audit outputs are themselves sensitive data.

Where it stops holding

Proxies form a continuum, not a bounded category: from pure stand-ins (group markers unrelated to the target) to legitimate strong signals (true predictors weakly tied to the group), with wide gray in between. Cleaning proxies is therefore ongoing monitoring rather than a one-time project — every feature expansion (new instrumentation, external data, new markets) imports new proxies. Over-cleaning has its own cost: deleting every feature correlated with sensitive attributes deletes the socioeconomic context itself, costing predictive power and the model's understanding of that context — making disparate-impact correction harder, not easier. The goal is distinguishing "uses a group marker" from "uses a real signal," not eliminating correlation.

Applying it

• Make proxy audits routine checkpoints: run single-feature and combined attribution detection on every feature-set change (new instrumentation, external data onboarding, market expansion).
• For identified strong proxies, run the orthogonal-component test to confirm whether the model leans on legitimate signal or group marker; remove the latter, retain the former with documented trade-offs.
• Write usage restrictions into external data contracts: no population-label intermediates (spending tiers, lifestyle clusters) in decision features.
• Verify: quarterly compare the proxy inventory's growth against output-gap trends; a new proxy coinciding with a widening gap triggers a dedicated attribution review.

Related

• Same group: P4.09.1 Dropping sensitive attributes does not equal equal outcomes · P4.09.4 Disparate impact is judged by outcome distributions, not intent
• Adjacent: P4.02 Choosing fairness definitions · O2.13 Third-party data and population labels
• Search terms: proxy variable · proxy discrimination · feature attribution audit