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Avoiding Discrimination through Causal Reasoning
Niki Kilbertus, Mateo Rojas-Carulla, Giambattista Parascandolo, Moritz Hardt, Dominik Janzing, Bernhard Schölkopf
TL;DR
Observational fairness criteria cannot generally determine whether predictors discriminate causally, even when predictors are Bayes optimal. The paper therefore frames fairness through causal graphs and interventions, introducing criteria and procedures for unresolved and proxy discrimination. Its conclusions depend on valid causal-graph construction and functional assumptions, while experimental validation remains outside scope.
Problem
Observational criteria based on joint distributions cannot generally distinguish intuitively different discrimination scenarios or determine unresolved discrimination.
Method
The paper uses causal graphs, resolving and proxy variables, and interventions to define causal non-discrimination criteria and develop removal procedures.
Results
The paper shows that observational criteria cannot generally determine unresolved discrimination in Bayes-optimal unconstrained or equal-odds predictors and gives an interventional characterization of proxy discrimination.
Takeaways & Limitations
Fairness analysis should focus on justified assumptions about the causal data-generating process rather than selecting a single statistical criterion.
Takeaways & Limitations
The framework assumes a valid causal graph, and proxy-discrimination removal depends on the functional form of causal dependencies; experimental validation is outside scope.
Abstract
from arXiv · showhide
Recent work on fairness in machine learning has focused on various statistical discrimination criteria and how they trade off. Most of these criteria are observational: They depend only on the joint distribution of predictor, protected attribute, features, and outcome. While convenient to work with, observational criteria have severe inherent limitations that prevent them from resolving matters of fairness conclusively. Going beyond observational criteria, we frame the problem of discrimination based on protected attributes in the language of causal reasoning. This viewpoint shifts attention from "What is the right fairness criterion?" to "What do we want to assume about the causal data generating process?" Through the lens of causality, we make several contributions. First, we crisply articulate why and when observational criteria fail, thus formalizing what was before a matter of opinion. Second, our approach exposes previously ignored subtleties and why they are fundamental to the problem. Finally, we put forward natural causal non-discrimination criteria and develop algorithms that satisfy them.
1 Introduction
The paper argues that observational fairness criteria cannot conclusively resolve discrimination, motivating a causal framework centered on assumptions about the data-generating process. It develops causal criteria and algorithms while distinguishing protected attributes from their proxies.
- Observational fairness criteria depend on the joint distribution of predictors, protected attributes, features, and outcomes, but competing criteria encode different opinions and trade-offs.
- Identical observed distributions can arise from intuitively different social scenarios, so no observational criterion can distinguish those scenarios.
- Its framework distinguishes protected-attribute concepts such as race or gender from algorithmically available proxies such as visual features or names.
- The paper introduces two intervention-based causal criteria for specific forms of discrimination and studies algorithms that avoid them.
- The paper shifts fairness analysis toward assumptions about the causal data-generating process rather than seeking one universally correct statistical criterion.
2 Unresolved discrimination and limitations of observational criteria
The paper defines unresolved discrimination through unblocked causal paths from a protected attribute to a predictor and shows that observational data generally cannot identify it. The Berkeley admissions example motivates distinguishing direct effects from effects mediated by accepted resolving variables.
- A resolving variable is an attribute influenced by the protected attribute in a manner accepted as nondiscriminatory, such as department choice in Berkeley admissions.
- Unresolved discrimination exists when a non-resolving variable has a directed path from A that is not blocked by a resolving variable.
- The skeptic viewpoint treats every path from A to R as problematic unless a resolving variable justifies it, motivating feature screening before constructing R.
- Demographic parity and equalized odds emerge as causal special cases when the resolving-variable set is empty or contains the true outcome Y.
- Two graphs can generate the same joint distribution while differing in whether a resolving variable blocks discrimination, illustrating the identification failure.
- No observational criterion can generally determine whether Bayes-optimal unconstrained or equal-odds predictors exhibit unresolved discrimination.
3 Proxy discrimination and interventions
The paper separates difficult-to-conceptualize protected-attribute interventions from observable proxies and defines proxy discrimination using interventions on those proxies. This yields a causal criterion and a procedure for removing proxy discrimination.
- Proxies are observable descendants of A that correlate substantially with A but, in the authors’ view, should not affect prediction.
- Potential proxy discrimination occurs when a path from A to a non-proxy variable is blocked by a proxy variable.
- Proxy discrimination is defined interventionally by requiring P(R | do(P = p)) = P(R | do(P = p′)) for all p and p′.
- The intervention do(P = p) removes incoming arrows to P and replaces its structural equation with P = p.
- The interventional criterion supports a procedure for removing proxy discrimination, while unawareness suffices when no directed path connects a proxy to a feature.
4 Procedures for avoiding discrimination
The paper constructs causal procedures that remove proxy or unresolved discrimination by intervening on causal graphs and imposing distributional invariance constraints. Under linearity and expressibility assumptions, these procedures yield non-discriminatory predictors, while unresolved-discrimination adjustment can remove legitimate resolving-variable effects when the predictor lacks access to the protected attribute.
- Avoiding proxy discrimination: Under expressibility and a suitable constant-in-P parameter choice, the procedure returns a non-trivial predictor with no proxy discrimination.The predictor can still use features that exhibit potential proxy discrimination.
- Avoiding proxy discrimination: The procedure intervenes on the relevant variable, rewrites the predictor using roots of the intervened graph, and imposes invariance of its distribution.For proxy discrimination, P is fixed; for unresolved discrimination, E is fixed to a random variable with E’s marginal distribution.
- Avoiding proxy discrimination: The proxy constraint is P(R | do(P = p)) = P(R | do(P = p′)), implemented by adjusting the direct P-to-R contribution against the mediated P-to-X-to-R influence.In the linear example, choosing θ0 can produce λP = −λXβ.
- Avoiding unresolved discrimination: For unresolved discrimination, intervention on E precedes cancellation of remaining A-to-R influence, but setting λX = 0 also removes the resolving path A → E → X → R.Without access to A, the predictor cannot adjust for unresolved discrimination while retaining resolved influences through X.
- Relating proxy discrimination to other fairness notions: Replacing E[X | do(P)] with E[X | P] is generally invalid because confounding can prevent observational regression from estimating the direct effect of P on X.The two expectations coincide only if at least one of A → P or A → X is absent.
- Relating proxy discrimination to other fairness notions: When all directed paths from ancestors of P to X are blocked by P, adjusted features X −E[X | P] support observationally learnable non-discriminatory predictors.This holds for the stated corollaries, including linear predictors and predictors under the stronger blocking condition involving paths to X.
- Relating proxy discrimination to other fairness notions: A linear predictor R = λ(X −E[X | do(P)]) + c exhibits no proxy discrimination in expectation.The result depends on the interventional expectation rather than the observational conditional expectation.
5 Conclusion
The paper frames fairness through causal reasoning, using assumptions about the data-generating process to address limits of statistical approaches. It develops causal criteria and procedures while acknowledging that validity depends on causal-model assumptions and that experimental validation is outside scope.
- Causal reasoning addresses shortcomings of earlier statistical fairness approaches by making causal data-generating assumptions explicit.
- The framework uses resolving and proxy variables to define causal discrimination criteria and develops a procedure for removing proxy discrimination under a structural equation model.
- Under linear structural equations, proxy-discrimination removal has an intuitive form resembling heuristics used in regression.
- The framework requires constructing a valid causal graph, and proxy-discrimination removal depends on the functional form of causal dependencies.
- Experimental validations are beyond the scope of the paper's conceptual and theoretical analysis.
Supplementary material
The supplementary material proves that observationally identical causal scenarios can differ in unresolved discrimination, then establishes conditions and adjusted-feature procedures for avoiding proxy discrimination. These results rely on structural assumptions such as additive linear influences and characterize when discrimination-free predictors must use adjusted representations.
- No observational criterion can generally determine unresolved discrimination for Bayes-optimal unconstrained or equal-odds predictors.
- Two causal graphs can generate the same joint distribution while differing in whether the optimal predictor exhibits unresolved discrimination.
- The equal-odds predictor is X2 because X2 is conditionally independent of A given Y, whereas using A or X1 violates equal odds.
- If no directed path connects a proxy to a feature, an unaware predictor based on that feature avoids proxy discrimination.
- With additive linear proxy influence on features, predictors based on adjusted features can avoid proxy discrimination, with observational learning possible under additional graph conditions.
- For linear predictors, subtracting the interventional feature expectation makes the expected prediction constant across proxy interventions.
- The supplementary derivations establish both sufficient and necessary conditions for discrimination-free predictor forms under the stated structural assumptions.
- Under additive linear assumptions and a smooth, strictly monotonic transformation, every predictor avoiding proxy discrimination has the characterized adjusted form.