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Fairness Through Causal Awareness: Learning Latent-Variable Models for Biased Data
David Madras, Elliot Creager, Toniann Pitassi, Richard Zemel
TL;DR
Historical decisions leave biased datasets with outcomes observed only for actions previously chosen, complicating fair decision-making. The paper models sensitive attributes as confounders and uses latent-variable inference to estimate causal effects. It reports better causal-effect estimates and evidence of more accurate, fairer policies, while noting that effects may remain unidentifiable when proxies cannot reveal confounders.
Problem
Fair decision-making requires reasoning about interventions and counterfactual outcomes, but historical data reflect past choices and sensitive attributes may shape treatments and outcomes.
Source: §1 · p. 1Method
The model treats the sensitive attribute as a confounder of treatment and outcome and uses latent-variable modeling with approximate inference for potential hidden confounders.
Source: §1 · p. 2, §6.2 · p. 7, §7 · p. 9Results
Takeaways & Limitations
Estimating sensitive-attribute causal effects can support treatment policies that are more accurate and fair in the reported historically biased-data setting.
Source: §1 · p. 2, §7 · p. 9If proxies cannot reveal all confounders, the joint distribution may not be learned and causal effects may be unidentifiable or inaccurate.
Source: §4 · p. 5
Abstract
from arXiv · showhide
How do we learn from biased data? Historical datasets often reflect historical prejudices; sensitive or protected attributes may affect the observed treatments and outcomes. Classification algorithms tasked with predicting outcomes accurately from these datasets tend to replicate these biases. We advocate a causal modeling approach to learning from biased data, exploring the relationship between fair classification and intervention. We propose a causal model in which the sensitive attribute confounds both the treatment and the outcome. Building on prior work in deep learning and generative modeling, we describe how to learn the parameters of this causal model from observational data alone, even in the presence of unobserved confounders. We show experimentally that fairness-aware causal modeling provides better estimates of the causal effects between the sensitive attribute, the treatment, and the outcome. We further present evidence that estimating these causal effects can help learn policies that are both more accurate and fair, when presented with a historically biased dataset.
1 INTRODUCTION
The introduction frames fair decision-making as intervention rather than outcome prediction, because historical data reveal only outcomes of actions already chosen. It proposes causal modeling that treats sensitive attributes as confounders and reports improved causal-effect estimates and more accurate, fairer policies.
1 INTRODUCTION
- Decision-making requires choosing actions, but historical data reveal outcomes only for actions previously taken, leaving counterfactual outcomes unobserved.The introduction argues that causal effects, rather than correlations alone, are needed to reason about decisions and counterfactuals.Source: §1 · p. 1
- Hidden confounders can obstruct exact causal-effect inference, while nonlinear outcomes and high-dimensional data complicate individual-level analysis.The paper presents its latent-variable approach as a way to model potential hidden confounders.Source: §1 · p. 1
- The proposed model combines causal modeling with approximate inference in deep latent-variable models to estimate individual causal effects from biased data.It models the sensitive attribute as potentially confounding both treatment and outcome.Source: §1 · pp. 1–2
- Experiments show the model outperforms non-causal models and causal models that omit sensitive-attribute confounding, and can support more accurate, fairer policies.The model also represents potential hidden confounders and complex, nonlinear relationships.Source: §1 · p. 2
2 BACKGROUND
The background distinguishes intervention-based causal reasoning from prediction on observational data, then introduces approximate inference for latent confounders and TARNet outcome models.
2.1 Causal Inference
- Structural causal models represent variables and causal relations through structural functions; an intervention sets treatment by removing its incoming arrows, unlike conditioning on observed data.Observational treatment assignment can be correlated with outcomes, so supervised prediction may misestimate treatment effects; typically, only one treatment outcome is observed per example.Source: §2.1 · p. 2
2.2 Approximate Inference
- When proxies are sufficiently informative, a latent variable Z can model unobserved confounders; amortized variational inference estimates Z, trading speed for less optimal inference.The approach weakens the no-hidden-confounders assumption, but identifiability depends on recovering the joint distribution from informative proxies.Source: §2.1 · p. 2, §2.2 · p. 3
2.3 TARNets
- TARNet uses two treatment-specific prediction arms with shared lower-layer parameters, and the paper does not use its group-wise MMD penalty.Only the arm corresponding to the treatment actually received gets an error signal for each example.Source: §2.3 · p. 3
3 FAIR CAUSAL INFERENCE
This section frames fairness-aware causal analysis around how sensitive attributes, treatments, and outcomes are related in historical data. It defines individual effects and explains how sensitive-attribute interventions are treated in the model.
3 FAIR CAUSAL INFERENCE
- Historical data may reflect sensitive attributes affecting treatments and outcomes; predictive policing illustrates how arrest data can preserve biased policing patterns.The paper treats causal effects as relevant to decision-making because they address intervention rather than correlation alone.Source: §3 · p. 3
- The framework considers sensitive attribute A, treatment T, outcome Y, and observed features X, using binary A and T despite recognizing this may be suboptimal in practice.The authors describe these variables as a minimal set for fairness-aware causal analysis, while noting that other domains may require richer models.Source: §3 · p. 3
- The individual treatment effect compares expected outcomes under T=1 and T=0, conditional on features X and sensitive attribute A.This effect is intended to indicate which treatment is likely to produce a favorable outcome for a given example.Source: §3 · p. 3
- The framework also asks how A affects treatment assignment and outcome, defining individual effects for A→T and conditional outcomes under interventions on A.These effects characterize potential bias in historical treatment assignment and outcomes.Source: §3 · p. 4
3.1 Intervening on Sensitive Attributes
- The authors regard causal effects of immutable attributes as valid in fairness analysis, and discuss interpreting them through manipulable proxies under specified assumptions [18].They cite constructivist approaches that treat race as having potentially manipulable constituent parts.Source: §3.1 · p. 4
- Although X may be post-treatment for A, the model uses observed covariates to infer latent Z; their correlation with A supports the abduction step in counterfactual computation.The authors describe this as adjusting for sensitive-attribute bias in the X-generating process.Source: §3.1 · p. 4
4 PROPOSED METHOD
The proposed model treats the sensitive attribute as a confounder of treatment and outcome, alongside latent confounders represented by Z. It learns a generative model and an inference model to estimate individual-level causal effects from observational data, subject to having informative proxies for confounders.
4 PROPOSED METHOD
- The model explicitly treats the sensitive attribute A as a confounder that can affect both treatment T and outcome Y, distinct from observed proxy features X.Latent Z represents other unobserved confounders; together, Z and A form the model’s confounding variables.Source: §4 · p. 4
- A flexible latent Gaussian and neural-network model represents confounders and nonlinear relationships, without claiming that Z is a definitive model of real-world confounders.Z follows the machine-learning convention of representing unspecified structure in the data rather than necessarily nameable objects.Source: §4 · pp. 4–5
- Causal effects require estimating outcomes under interventions, but Z is unobserved and must be inferred from observed proxies X.The model estimates interventional outcomes by applying the structural functions under specified values of A and T.Source: §4 · p. 5
- Deep-network variational inference jointly learns a generative model of the data and an inference model for Z given X and A.The inference network does not use treatment or outcome as inputs; A is observed and need not be inferred.Source: §4 · pp. 5–6
- The model assumes sufficiently informative proxies: at least one proxy is needed for each confounder to recover the joint distribution and identify causal effects.If some confounders cannot be inferred from X, effects may be unidentifiable and estimates inaccurate; collecting additional proxies is one proposed response.Source: §4 · p. 5
5 RELATED WORK
The paper situates its approach among work on causal effects, fairness, and biased data. It distinguishes its sensitive-attribute-aware causal model from related methods with different modeling goals or assumptions.
5 RELATED WORK
- The closest related model, the Causal Effect Variational Autoencoder, does not include a sensitive attribute; the authors also distinguish their model from a discriminative information-bottleneck approach.The latter also lacks a reconstruction-fidelity term; prior deep causal-effect work by Shalit et al. [44] and Johansson et al. [19] assumes observed confounders.Source: §5 · p. 6
- Related fairness-and-causality work studies counterfactual fairness, fairness criteria for treatments, fair interventions [28], and causal decompositions of unfairness.Other work examines causal relationships between sensitive attributes and proxies in fair classification [21].Source: §5 · p. 6
- Work on biased data notes that a fair predictor may fail under some distribution shifts [20], while selective-label research studies biased availability of outcome labels [9].Related threads also examine feedback loops in predictive policing [12] and recommender systems.Source: §5 · p. 6
- Barabas et al. [3] frame many fair-prediction problems as interventions, while Louizos et al. [31] pursue fair representation learning rather than causal modeling.Dwork et al. [10] introduced “fairness through awareness” and argued for giving sensitive attributes a privileged modeling role.Source: §5 · p. 6
6 EXPERIMENTS
On semi-synthetic IHDP data, the experiments compare fair-aware causal models with causal and prediction-focused alternatives. The FCVAE estimates sensitive-attribute effects favorably and yields policies with lower regret and accuracy gaps.
6.1 Data.
- The evaluation adapts the semi-synthetic IHDP benchmark, using the mother's race as a binary sensitive attribute and constructing counterfactual outcomes and treatments.The authors use semi-synthetic data because validating causal effects requires randomized trials, while randomizing a sensitive attribute is usually impossible.Source: §6.1 · pp. 6–7
6.2 Experimental Setup.
- FCVAE models A as a confounder of treatment and outcome, unlike prediction-focused MLP baselines and CVAE-A, which models treatment effects but treats A as a covariate.FCVAE is tested in two versions, differing in whether A helps reconstruct X and infer Z.Source: §6.2 · p. 7
6.3.1 Estimating Causal Effects.
- PEHE evaluates individual-level causal-effect estimates by comparing modeled and ground-truth differences in factual and counterfactual results.Effects are conditioned on observed X, and possibly A, then averaged across the dataset.Source: §6 · p. 6, §6.3.1 · p. 7
- As informative proxies are removed, PEHE rises for the more complex A→Y and T→Y estimates; A→T varies less because it has no extra confounders or mediators.The feature-removal settings remove up to two of the most informative features, measured by correlation with the hidden confounder.Source: §6.3.1 · pp. 7–8
- FCVAE-1 and FCVAE-2 have lower PEHE than the other models for A→Y and A→T, and perform similarly to CVAE-A for T→Y.The T→Y comparison shows a slight FCVAE improvement in the settings with one or two informative features removed.Source: Table 1 · p. 8, Table 2 · p. 8, Table 3 · p. 8
6.3.2 Learning a Treatment Policy.
- The fair-aware model achieves lower policy regret than the unaware causal model and much lower regret than non-causal models in both IHDP settings.The comparison covers easier and more difficult settings with useful covariates removed.Source: §6.3.2 · p. 8, Table 5 · p. 9
- FCVAE achieves a smaller treatment-selection accuracy gap than models that do not account for the sensitive attribute's effect.The paper treats a smaller gap in subgroup accuracy as a fairer policy.Source: Table 6 · p. 9, §6.3.2 · p. 9
7 DISCUSSION
The paper models sensitive attributes as observed confounders and uses deep latent-variable models to infer hidden confounders. It outlines research directions enabled by estimating causal effects and counterfactual outcomes.
7 DISCUSSION
- The model treats the sensitive attribute as an observed confounder and uses deep latent-variable models to approximately infer other hidden confounders.The discussion presents this as the paper’s approach to learning from potentially biased data.Source: §7 · p. 9
- The authors report that their model learned a simple treatment policy that assigned treatments more accurately and fairly than several causal and non-causal baselines.They frame the intervention-focused approach as potentially supporting more equitable deployment when only biased data are available.Source: §7 · pp. 9–10
- Counterfactual outcomes for both treatment and sensitive attribute could support policies that assess everyone under a shared sensitive-attribute value, as well as fair missing-data imputation.The discussion also proposes decomposing the sensitive attribute’s effect on outcomes into direct and treatment-mediated effects, and using estimated effects for historical-bias audits and constrained policy learning.Source: §7 · p. 9
- The discussion connects specifying prior knowledge in graphical models to learning distributions over datasets that share global parameters, an AutoML task.The AutoML connection is stated in the continuation of the prior-knowledge discussion.Source: §7 · pp. 9–10
A DATA GENERATION
The appendix describes dataset generation and lists parameter settings for its algorithm. It specifies categorical distributions for β variables and values for several constants.
A DATA GENERATION
- Algorithm 1’s subroutines generate factual and counterfactual outcomes and treatments for each example under possible settings of A and T.The passage denotes the outcome under interventions do(T = t), do(A = a) as yT=t,A=a.Source: A DATA GENERATION · p. 12
- For binary variables, β_i is sampled from {0, 0.1, 0.2, 0.3, 0.4} with probabilities {0.6, 0.1, 0.1, 0.1, 0.1}; for Z, it uses {0.4, 0.6} with equal probabilities.For the other specified variables, the probabilities are {0.5, 0.125, 0.125, 0.125, 0.125} over {0, 0.1, 0.2, 0.3, 0.4}.Source: A DATA GENERATION · p. 12
- The listed constants are β_A = 6, ω = −11, and α_0, α_1, ζ = 0.7, 0.4, 0.1.The passage defines Cat(x,p) as selecting values from x according to probabilities p and notes that the algorithm also uses Clip.Source: A DATA GENERATION · p. 12
B IDENTIFIABILITY OF CAUSAL EFFECTS
The appendix argues that recovering the joint distribution P(Z, A, X, T, Y) allows recovery of the treatment effects of interest. It outlines an identifiability proof for the treatment effect on the outcome.
B IDENTIFIABILITY OF CAUSAL EFFECTS
- Recovering P(Z, A, X, T, Y) is sufficient to recover the effects T → Y, A → T, and A → Y.The passage defines these as contrasts between expected outcomes or treatments under interventions, conditional on the stated variables.Source: B IDENTIFIABILITY OF CAUSAL EFFECTS · p. 12
- The proof focuses on identifying E(Y | do(T = 1), X, A); the authors say the arguments for the other effects are similar.The proof follows Louizos et al. [30] and reduces the expression using the do-calculus.Source: B IDENTIFIABILITY OF CAUSAL EFFECTS · p. 12
- Once the joint distribution is known, each term in the reduced expression can be identified, which identifies the treatment-effect expression.The theorem states recovery of the joint distribution under the causal model in Fig. 1d as its condition.Source: B IDENTIFIABILITY OF CAUSAL EFFECTS · p. 12
C EXPERIMENTAL DETAILS
The experiments use repeated seed pairs, neural-network parameterizations, and posterior sampling. Training uses validation ELBO for early stopping, while test predictions average repeated samples.
C EXPERIMENTAL DETAILS
- Each model is run on 500 data-seed/model-seed pairs to estimate error confidence robustly.The causal-model functions use neural networks; the learned hidden confounder Z has 10 units, and the X–Z networks have one 20-unit hidden layer.Source: C EXPERIMENTAL DETAILS · p. 12
- Each TARNET uses a network producing a shared representation and two prediction networks; each prediction network has one hidden layer with 100 units, and the shared representation has 20 units.Source: C EXPERIMENTAL DETAILS · p. 12
- Training averages the ELBO over 10 posterior samples and stops after 10 validation epochs without improvement; test predictions average 10 samples.The passage notes a unit-variance assumption for X, normalized during preprocessing.Source: C EXPERIMENTAL DETAILS · pp. 12–13