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Demographic parity in regression and classification within the unawareness framework

NeurIPS 2026 · Learning theory and algorithms › Fairness · approach: Minimax fairness via sampling · 0 citations (OpenAlex)

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Characterizes the optimal demographic-parity-constrained quadratic-loss regression under the unawareness framework as an optimal-transport barycenter, and shows that equivalence with thresholded cost-sensitive classifiers holds exactly when the problem is nested.

Problem

Fair regression and classification under demographic parity when the sensitive attribute cannot be used directly (unawareness framework), where the optimal fair regression function and its link to fair classifiers were previously uncharacterized.

Approach

Reformulates the unaware fair regression problem as a barycenter problem with multi-to-one dimensional optimal transport costs over (η(X), Δ(X)), proves existence of a transport-map solution, and shows the regression function can be recovered from nested cost-sensitive classifiers if and only if a nestedness condition holds.

Key results

• Under Assumption 1, the optimal unaware fair regression function exists and is given by a transport-map solution to the barycenter problem over (η(X), Δ(X)), so f* depends on x only through η(x) and Δ(x), an estimate of group membership.
• Proposition 1 shows that, under mild assumptions, the optimal unaware fair regression function does not preserve order when the Bayes regression function violates demographic parity.
• Theorem 5: if the classification problem is nested, the regression function f*(x)=sup{y: g_y(x)=1} is optimal; conversely, non-nestedness implies some thresholded classifier is suboptimal (Proposition 6).

Surprising findings

• The optimal fair regression function in the unawareness framework does not preserve order in general, so highly qualified members of protected groups may be penalized by the fairness correction.
• The optimal fair classifier under unawareness is generally not envy-free within group, unlike in the awareness framework.

Limitations

• Results restricted to a binary sensitive attribute (S = {1, 2}).
• Applies only to univariate regression targets.
• No explicit closed form for the optimal fair regression function; nestedness is not always satisfied.

Experimental setup

Builds on: Chzhen and Schreuder optimal fair regression (awareness) Gaucher, Schreuder, Chzhen fair classification (awareness) Le Quy et al. fairness datasets (LMC18 empirical) Agarwal, Dudik, Wu reduction to cost-sensitive classification Chiappa-Gordaliza-Tsamados-Ziegler-style cost-sensitive nestedness (Chzhen-Schre

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