PaperlayerView exact revision on arXiv

Source-linked AI summary

Path-Specific Counterfactual Fairness

Silvia Chiappa, Thomas P. S. Gillam

arXiv:1802.08139v1stat.ML

TL;DR

The paper addresses fair decision-making when a sensitive attribute affects outcomes through both fair and unfair pathways. It proposes correcting descendants along unfair pathways rather than constraining model parameters, retaining fair information and supporting complex non-linear settings. The approach is presented as simplifying, generalizing, and outperforming previous literature.

  • Problem

    Fair decision systems must distinguish unfair from fair causal effects of sensitive attributes, while existing path-specific-effect computation can be intractable and may lose predictive information.

  • Method

    The method corrects variables that are descendants of the sensitive attribute along unfair pathways, using deep learning and approximate inference instead of parameter constraints.

  • Results

    The paper reports that its latent inference-projection method simplifies, generalizes, and outperforms previous literature for path-specific counterfactual fairness.

  • Takeaways & Limitations

    Correcting unfair information while retaining fair information leaves the underlying data-generation mechanism unaltered and avoids completely discarding problematic descendants.

  • Takeaways & Limitations

    The method’s fairness is most likely not achieved when the learned model’s assumed data-generation process mismatches the process underlying the observations.

Abstract

from arXiv · show

We consider the problem of learning fair decision systems in complex scenarios in which a sensitive attribute might affect the decision along both fair and unfair pathways. We introduce a causal approach to disregard effects along unfair pathways that simplifies and generalizes previous literature. Our method corrects observations adversely affected by the sensitive attribute, and uses these to form a decision. This avoids disregarding fair information, and does not require an often intractable computation of the path-specific effect. We leverage recent developments in deep learning and approximate inference to achieve a solution that is widely applicable to complex, non-linear scenarios.

1. Introduction

Fairness can require distinguishing fair from unfair causal pathways rather than removing all sensitive-attribute influence. The paper proposes correcting unfairly affected descendants while retaining fair information, avoiding parameter constraints and often intractable path-specific-effect computation.

  • Machine-learning decisions can amplify societal bias in sensitive domains such as policing, education, hiring, lending, and criminal-risk assessment.
  • Statistical fairness criteria may conflict, and observational approaches may fail to distinguish correlation from causation or different causal pathways.
  • Counterfactual fairness treats the entire sensitive-attribute effect as problematic, although practical cases may contain fair pathways.
  • Path-specific counterfactual fairness requires disregarding effects along unfair pathways while preserving effects along fair pathways.
  • Earlier methods constrain model parameters or conditional distributions, rely on linear relations, and may remove predictive information from descendants of the sensitive attribute.
  • The proposed method corrects descendants affected through unfair pathways, retaining fair information and supporting complex, non-linear scenarios through deep learning and approximate inference.

2. Background on Causality

Graphical causal models represent variables and their causal relationships, allowing direct, potential, and confounded effects to be distinguished. Interventions remove confounding links and define causal effects through potential outcomes.

  • Graphical Causal Models represent variables as nodes and statistical or causal relationships as directed links.
  • A variable is a direct cause of Y when it is Y’s child, and a potential cause when Y is its descendant.
  • Causal effects follow directed paths and equal p(Y|A) only when open noncausal paths between A and Y are absent.
  • A confounder creates an open noncausal path, such as A←C→Y, so conditioning on A alone does not identify the causal effect.
  • Intervening on A fixes its value, removes the confounder-to-A link, and leaves the other conditional distributions unchanged.
  • The resulting intervened distribution defines the potential outcome variable Y_A=a, commonly abbreviated Y_a.

3. Causal Effect along Different Pathways

The paper separates a sensitive attribute’s causal influence into fair and unfair pathways, defining fairness by limiting the effect along unfair pathways. It proposes intervening on the sensitive attribute along those pathways to remove the path-specific effect without discarding fair information or explicitly computing an often intractable quantity.

  • Path-specific counterfactual fairness requires the difference between the sensitive attribute’s causal effects along unfair pathways to be small.The path-specific effect (PSE) is the average of this difference, under binary sensitive-attribute values with one baseline value.
  • Explicitly computing and constraining the PSE can be intractable beyond linear or low-dimensional scenarios and can discard predictive information from unfair-pathway descendants.The earlier approach also relies on approximations and linearity assumptions, while averaging over descendants affected through unfair pathways.
  • The proposed correction intervenes on the sensitive attribute, setting it to the baseline value along unfair pathways to remove the PSE while retaining fair information in affected descendants.This removes the path-specific effect implicitly rather than requiring its explicit computation.
  • 3.1. Direct and Indirect Effect: For direct and indirect effects, the method uses counterfactual variables that assign different sensitive-attribute values along selected causal paths.With one indirect path through M, Ya(M(a′)) applies A = a along the direct path and A = a′ along the indirect path; ADE and AIE are then defined from such counterfactuals.
  • 3.1. Direct and Indirect Effect: Under sequential ignorability and no confounders, counterfactual distributions can be estimated from observed conditional distributions; confounding requires conditioning on C.If C is unobserved, the relevant effect may be non-identifiable through simple observed-data methods, although latent-variable likelihood methods may learn the distributions.
  • 3.1. Direct and Indirect Effect: For arbitrary path sets, a recursive rule sets variables to baseline or path-specific counterfactual values according to whether incoming edges are unfair or fair.The resulting counterfactual variable represents the selected path effect, but identification can fail when required confounders are unobserved.

4. Path-Specific Counterfactual Fairness

The approach achieves path-specific fairness by correcting descendants of the sensitive attribute along unfair pathways while retaining fair information. It uses latent inference, projection, and approximate inference to extend this strategy to complex, non-linear models, while noting sensitivity to model–observation mismatch.

  • For the target graph, unfair effects include the direct path A →Y and paths passing through M, while dashed green-black paths are unfair only through A →M.The desired counterfactual uses baseline A along these unfair pathways while retaining other pathway effects.
  • Earlier parameter-constraint approaches can discard individual-specific information by integrating out or canceling variables such as M and L, and their extension to complex scenarios is unclear.The proposed correction instead aims to retain fair information within those descendants.
  • The method forms fair predictions by correcting descendants of A along unfair paths rather than imposing constraints on model parameters.This preserves fair information in problematic descendants and leaves the underlying data-generation mechanism unaltered.
  • Model–observation mismatch can undermine fairness when unmodeled effects are absorbed into noise, making the noise dependent on A.Introducing explicit latent variables for descendants such as M addresses this issue, with MMD encouraging their inferred distributions to depend little on A.
  • The general method uses latent variables and variational approximations for otherwise intractable likelihoods and posteriors, then forms fair predictions with Monte Carlo samples.The approach jointly learns latent embeddings and predictive distributions, supporting categorical or continuous descendants through flexible conditional models.

5. Experiments

Experiments test latent inference-projection on Berkeley Admission, UCI Adult, and German Credit data, evaluating whether unfair pathway information can be removed while retaining accuracy. Results show near-target accuracy on Berkeley, accuracy–fairness trade-offs on Adult, and stable fairness and accuracy across German Credit training stages.

  • 5.1. The Berkeley Admission Dataset: The modified Berkeley dataset added a direct A →Y bias path, raising accuracy from 67.9% using D →Y alone to 71.6% using both pathways.This construction tests whether the method can disregard unfair information that materially affects predictions.
  • 5.2. The UCI Adult Dataset: On UCI Adult, constraining the PSE between 0.95 and 1.05 reduced test accuracy to 72%, compared with 82% for the unconstrained case.The Adult setup predicts income above or below $50,000 and omits race and capital gain and loss to match prior work.
  • 5.3. The UCI German Credit Dataset: On UCI German Credit, unfair and fair accuracy and MMD for Hs remained similar after 2,000, 4,000, and 8,000 training steps.The authors report that the learned structured distribution did not differ significantly between females and males, with housing showing the largest remaining difference.

6. Conclusions

The paper concludes that latent inference-projection achieves path-specific counterfactual fairness by correcting descendants along unfair pathways rather than constraining model parameters. This retains fair information, leaves the data-generation mechanism unchanged, and is presented as applicable to complex settings.

  • 6. Conclusions: The latent inference-projection method corrects protected-attribute descendants along unfair pathways instead of imposing constraints on model parameters.The approach is described as simplifying, generalizing, and outperforming previous literature.
  • 6. Conclusions: The correction retains fair information in problematic descendants and leaves the underlying data-generation mechanism unaltered.The authors identify alternative techniques to MMD for enforcing independence between latent variables and the sensitive attribute as future work.

A. Identifiability of PSE

This appendix defines graph-based concepts used to establish whether a path-specific effect is identifiable. It introduces ADMGs, districts, and recanting districts as structural criteria for analyzing causal pathways.

  • A. Identifiability of PSE: The appendix summarizes a graphical method for determining whether a path-specific effect is identifiable.The criterion is based on the causal graph structure and the presence of recanting districts.
  • A. Identifiability of PSE: An ADMG is a causal graph with directed links and red bidirected links representing unobserved common causes.Directed links may be marked according to whether their causal paths are of interest.
  • A. Identifiability of PSE: The district of A is the set of nodes reachable from A through bidirected paths.In the example, the district of Y is {M, Y}.
  • A. Identifiability of PSE: A recanting district is a district containing nodes reached from A along both selected and unselected causal paths to Y.The example district {M, Y} is recanting for the direct A →Y effect because A →M →Y is excluded from the selected path set.

B. Latent-Variable Conditional Distribution

The latent-variable appendix characterizes conditional latent distributions for the model and illustrates them with Gaussian latent variables and mixture priors. These distributions support inference of latent representations conditioned on the sensitive attribute and observed variables.

  • B. Latent-Variable Conditional Distribution: Adding a Gaussian latent variable Hm to the equation for M yields a Gaussian joint distribution p(Z={Y,L,M,C,Hm}|A).The exponent of this joint distribution is proportional to a quadratic form.
  • B. Latent-Variable Conditional Distribution: The conditional distribution p(Hm|A,C,M,L) is computed using Gaussian marginalization and conditioning formulas.This provides the latent conditional needed for the model's inference procedure.
  • B. Latent-Variable Conditional Distribution: Figure 8 compares two-dimensional Hm and Hl distributions and a six-dimensional Hr distribution after 5,000 training steps with their corresponding mixture-of-ten-Gaussians priors.Panel (a) shows learned conditional latent distributions, while panel (b) shows the associated priors.

C. Experimental Details

The experiments use mixture-of-Gaussians priors and neural-network parameterizations for variational posteriors and conditional distributions.

  • Each latent variable uses a prior formed by a ten-component mixture of two-dimensional Gaussians with diagonal covariances.
  • The variational posterior is a two-dimensional diagonal-covariance Gaussian whose means and log variances come from a neural network.The network uses two size-20 linear layers with tanh activation followed by a linear layer.
  • The conditional distributions use fθ implemented as a neural network.

C.1. UCI Adult Dataset

The UCI Adult experiment visualizes prior and posterior latent-space distributions, including posterior histograms across selected variables and training stages.

  • The experiment presents histograms for prior and posterior distributions in the latent space.
  • Figure 9 compares posterior histograms after 2,000 and 8,000 training steps.
  • The figure covers checking-account status and savings with two dimensions each, plus housing with one dimension.

C.2. UCI German Credit Dataset

The UCI German Credit experiment reports posterior-distribution histograms in the latent space, with Figure 9 organizing results by training stage and variable.

  • The experiment shows histograms for posterior distributions in the latent space.
Loading 1802.08139v1…