[Paper Review] Optimal Training of Fair Predictive Models

Razieh Nabi, Daniel Malinsky+1 more|arXiv (Cornell University)|Oct 9, 2019

Ethics and Social Impacts of AI26 references4 citations

TL;DR

This paper proposes a novel reparameterization of the observed data likelihood to embed fairness constraints—specifically path-specific causal effects—directly as parameters in the likelihood function, transforming complex nonlinear constraints into simple box constraints. By combining this with empirical likelihood techniques to constrain baseline covariates, the method improves predictive accuracy while enforcing fairness, achieving performance close to unconstrained models in simulations.

ABSTRACT

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific causal constraints proposed by Nabi and Shpitser (2018), we introduce new theoretical results and optimization techniques to make model training easier and more accurate. Specifically, we show how to reparameterize the observed data likelihood such that fairness constraints correspond directly to parameters that appear in the likelihood, transforming a complex constrained optimization objective into a simple optimization problem with box constraints. We also exploit methods from empirical likelihood theory in statistics to improve predictive performance by constraining baseline covariates, without requiring parametric models. We combine the merits of both proposals to optimize a hybrid reparameterized likelihood. The techniques presented here should be applicable more broadly to fair prediction proposals that impose constraints on predictive models.

Motivation & Objective

• To address the challenge of training fair predictive models under complex, nonlinear fairness constraints derived from causal path-specific effects.
• To simplify constrained optimization by reparameterizing the likelihood so fairness constraints appear as explicit, easily constrained parameters.
• To improve predictive performance by incorporating empirical likelihood methods to constrain baseline covariates without assuming parametric models.
• To develop a hybrid approach that combines reparameterization and empirical likelihood for more efficient data usage and better accuracy.
• To demonstrate the generalizability of the method to other fairness-constrained prediction problems beyond the specific causal framework studied.

Proposed method

• Reparameterize the observed data likelihood such that unfair path-specific effects become explicit parameters in the likelihood, allowing fairness constraints to be enforced as simple box constraints on these parameters.
• Use empirical likelihood theory to construct a semi-parametric likelihood that constrains the distribution of baseline covariates, improving data efficiency and predictive accuracy.
• Formulate a hybrid likelihood that combines the reparameterized likelihood with empirical likelihood constraints on covariates, enabling joint optimization of fairness and prediction.
• Apply the method to a causal model where the outcome depends on mediators and sensitive attributes, with fairness enforced by restricting direct and indirect path-specific effects.
• Use constrained maximum likelihood estimation (MLE) with the reparameterized and hybrid likelihoods, optimizing over both likelihood parameters and empirical likelihood weights.
• Leverage the g-formula and inverse probability weighting (IPW) as benchmarks to evaluate the performance of the proposed methods in terms of KL divergence and mean squared error (MSE).

Experimental results

Research questions

• RQ1 Can path-specific fairness constraints be embedded directly into the likelihood function as parameters to simplify constrained optimization in predictive modeling?
• RQ2 How does reparameterizing the likelihood to make fairness constraints explicit affect predictive accuracy compared to standard constrained MLE?
• RQ3 To what extent can empirical likelihood techniques improve fairness-aware prediction by constraining baseline covariates without parametric assumptions?
• RQ4 Does combining reparameterization with empirical likelihood lead to better predictive performance than either method alone?
• RQ5 Can the proposed hybrid approach achieve fairness with minimal sacrifice in predictive accuracy, approaching the performance of unconstrained models?

Key findings

• The reparameterized MLE method (M2) reduced the KL divergence to the true unfair distribution by 1.5% compared to standard constrained MLE (M1), though it offered only minimal improvement in MSE.
• The hybrid MLE method (M3) achieved a 66% reduction in MSE compared to the standard constrained MLE (M1), dropping from 3.497 to 1.166 in simulation 1.
• The hybrid reparameterized MLE (M4) further improved MSE to 1.569 in simulation 1, demonstrating the benefit of combining reparameterization with empirical likelihood for covariate constraints.
• In simulation 3 with multiple mediators, the hybrid MLE reduced MSE from 2.484 (baseline constrained MLE) to 1.131, showing substantial gains in predictive accuracy under fairness constraints.
• The method achieved a fair distribution (p*) with a path-specific effect (PSE) restricted to [-0.05, 0.05], while maintaining a KL divergence close to that of the unconstrained model, indicating strong fidelity to the data distribution.
• The proposed hybrid approach outperformed all baseline methods in both fairness enforcement and predictive accuracy, with the lowest MSE and a fair PSE estimate of 0.02 in simulation 1.