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Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder
Hyemi Kim, Seungjae Shin, JoonHo Jang, Kyungwoo Song, Weonyoung Joo, Wanmo Kang, Il-Chul Moon
TL;DR
Single-latent causal models do not distinguish intervention-caused information from information merely correlated with the intervention, complicating fair counterfactual generation. DCEVAE disentangles these sources of uncertainty and reports more accurate effect estimates than single-latent causal VAEs. It also produces fair counterfactual examples with less transformation of the original data.
Problem
Single-latent causal models cannot distinguish information caused by the sensitive intervention from information merely correlated with it.
Source: Introduction · p. 2Method
DCEVAE disentangles exogenous uncertainty into latent variables for intervention-caused information and information from features not caused by the intervention.
Source: Introduction · p. 2Results
DCEVAE estimates total and counterfactual effects more accurately than causal VAE models with a single latent.
Source: Introduction · p. 2Takeaways & Limitations
With fairness regularization, DCEVAE generates counterfactual fair examples with less transformation of the original dataset.
Source: Introduction · p. 2The causal setup allows some features to precede the sensitive attribute and others to follow it, rather than requiring all features to precede it.
Source: Causal Structure of Disentangled… · p. 3
Abstract
from arXiv · showhide
The problem of fair classification can be mollified if we develop a method to remove the embedded sensitive information from the classification features. This line of separating the sensitive information is developed through the causal inference, and the causal inference enables the counterfactual generations to contrast the what-if case of the opposite sensitive attribute. Along with this separation with the causality, a frequent assumption in the deep latent causal model defines a single latent variable to absorb the entire exogenous uncertainty of the causal graph. However, we claim that such structure cannot distinguish the 1) information caused by the intervention (i.e., sensitive variable) and 2) information correlated with the intervention from the data. Therefore, this paper proposes Disentangled Causal Effect Variational Autoencoder (DCEVAE) to resolve this limitation by disentangling the exogenous uncertainty into two latent variables: either 1) independent to interventions or 2) correlated to interventions without causality. Particularly, our disentangling approach preserves the latent variable correlated to interventions in generating counterfactual examples. We show that our method estimates the total effect and the counterfactual effect without a complete causal graph. By adding a fairness regularization, DCEVAE generates a counterfactual fair dataset while losing less original information. Also, DCEVAE generates natural counterfactual images by only flipping sensitive information. Additionally, we theoretically show the differences in the covariance structures of DCEVAE and prior works from the perspective of the latent disentanglement.
Introduction
DCEVAE addresses the limits of single-latent causal models by separating intervention-caused information from other exogenous uncertainty. This separation supports counterfactual generation that changes relevant attributes while preserving others, and the paper reports improved effect estimation and less transformation of the original data.
Introduction
- Counterfactual images should alter intervention-descendant attributes while preserving other attributes; the figure contrasts DCEVAE's preservation with CEVAE and mCEVAE's failures to maintain irrelevant attributes.For example, changing the smiling label may also change descendant attributes such as mouth openness or eye shape.Source: Figure 1 · p. 1
- Causal inference frames fairness as estimating how a sensitive intervention affects individual features and an outcome.The paper treats sensitive attributes such as race and gender as intervention variables.Source: Introduction · p. 1
- DCEVAE separates exogenous uncertainty into latent variables for information caused by the intervention and information from features not caused by it.The paper contrasts this with prior single-latent approaches that model all features together.Source: Introduction · p. 2
- DCEVAE estimates total and counterfactual effects more accurately than single-latent causal VAE models, and fairness regularization yields fair examples with less transformation of the original dataset.The paper also reports counterfactual images with attributes, such as women with mustaches, that do not naturally occur in the dataset.Source: Introduction · p. 2
Preliminaries
Counterfactual fairness compares predicted outcomes under different sensitive-attribute values for the same individual. Prior causal VAEs can entangle intervention effects with other information, motivating a model that disentangles latent factors while retaining information merely correlated with the intervention.
Counterfactual Fairness Problem Formulation
- Counterfactual fairness requires an individual's estimated outcome distributions to remain identical across attainable sensitive-attribute values.The formulation distinguishes sensitive attributes A, other observed attributes X, outcome Y, and estimate Ŷ.Source: Counterfactual Fairness Problem… · p. 2
Causality with Variational Autoencoder
- CEVAE can embed the intervention's causal influence in its single latent, obstructing counterfactual generation; mCEVAE's MMD regularization also removes latent components merely correlated with the intervention.DCEVAE's motivation is to retain those correlated components while separating intervention-caused features from other features.Source: Causality with Variational Autoencoder · p. 2
Disentanglement with Total Correlation
- Total correlation measures dependence among latent dimensions, and minimizing it is used to make the latent variable disentangled.The text defines a disentangled latent as one whose dimensions are independent.Source: Disentanglement with Total Correlation · p. 3
Methodology
DCEVAE separates intervention-caused features from other features, encoding their exogenous uncertainty in distinct latent variables. It uses these variables to generate counterfactuals that change intervention-dependent features while retaining other features, with disentanglement and fairness objectives shaping the model.
Causal Structure of Disentangled Causal Effect Variational Autoencoder
- DCEVAE partitions features into intervention-caused xd and other xr, assigning them ud and ur; ud is disentangled from a, while ur may retain information correlated with a.The causal ordering allows some features to precede a and others to follow it: intervening on gender can change school but not birth year.Source: Causal Structure of Disentangled… · p. 3
Bayesian Network of Disentangled Causal Effect Variational Autoencoder
- The Bayesian network maps the two exogenous variables to latent variables, infers them with two encoders, and optimizes an ELBO plus total-correlation disentanglement through a min-max objective.A discriminator estimates total correlation, LT C, while the model objective is optimized against it.Source: Bayesian Network of Disentangled… · p. 3
Counterfactual Inference and Counterfactual Example Generation
- Counterfactual inference abducts ud and ur from the encoder, substitutes ¬a, then predicts with p(y|¬a, ud, ur), allowing xd to change while xr remains fixed.Under the stated causal model, recovering the joint distribution p(ud, ur, a, xd, xr, y) recovers the counterfactual effect.Source: Counterfactual Inference and… · p. 4
Evidence Lower Bound of DCEVAE
- The ELBO factorization assumes xd and ur are independent given ud, and xr and (a, ud) are independent given ur; Gaussian latent distributions are inferred by neural-network layers.The decoder models xd and y as influenced by a, while xr is determined by ur rather than a.Source: Evidence Lower Bound of DCEVAE · p. 4
- For counterfactual decoding, DCEVAE reuses its encoder and decoder but flips a to ¬a, keeping xr the same while xd and y respond to the intervention.Source: Evidence Lower Bound of DCEVAE · p. 4
Disentanglement Loss of DCEVAE
- The disentanglement loss minimizes dependence between a and ud and between ud and ur, approximating an intractable KL divergence with a discriminator and permutation-based sampling.The discriminator uses a density-ratio trick to distinguish samples from q(a, ud, ur) and q(a, ur)q(ud).Source: Disentanglement Loss of DCEVAE · p. 4
Theoretic Analysis on Covariance Structure
- DCEVAE’s covariance has distinct ur and ud blocks; as β approaches infinity, the stationary covariance becomes block diagonal, whereas CEVAE shows no covariance disentanglement.Figure 3 displays sampled latent covariance matrices for DCEVAE at β=0 and 1000 and for CEVAE’s two decoders.Source: Theoretic Analysis on Covariance… · p. 5, Figure 3 · p. 5
Application
- The fairness application adds a regularizer to DCEVAE’s objective, then trains a classifier on decoded predictions for both a and ¬a; image generation instead decodes with ¬a from inferred latents.Source: Application · p. 5
Experiments
The experiments use UCI Adult for causal-effect estimation and fair classification, and CelebA for counterfactual image generation. Evaluation covers effect estimation, generated-data similarity and classifier accuracy, alongside image semantics, distribution, and identity preservation.
Datasets and Baselines
- UCI Adult experiments treat gender as the intervention, income as the outcome, race, age, and native country as xr, and other variables as xd; CelebA experiments intervene on Mustache.The causal-estimation baselines include CausalGAN, CausalGAN-IC, CVAE, CEVAE, and mCEVAE; fairness and image-generation evaluations use additional baselines.Source: Datasets and Baselines · p. 5
Evaluation Metrics
- Causal and fairness evaluation measures total and counterfactual effects, generated-data chi-square distance, and test accuracy of logistic-regression and SVM classifiers trained on generated data.Total effect measures the change in outcome likelihood across interventions; counterfactual effect conditions that change on an observation.Source: Evaluation Metrics · p. 6
- Counterfactual image quality is evaluated by preservation of xr attributes, Frechet Inception Distance, and face-match identity preservation.The face-matching evaluation uses 1,544 Mustache pairs and 10,000 Smiling pairs.Source: Evaluation Metrics · p. 6
Results
DCEVAE estimates causal effects and supports fair classification without a complete causal graph. On image generation, it preserves identity and unrelated attributes while changing the intervention attribute, and leads on several reported quality measures.
Causal Estimation and Fairness Task
- On UCI Adult, DCEVAE estimates total and counterfactual effects close to the original data without knowing the exact causal graph; with fairness regularization, its accuracy, TE, and CE are comparable to CFGAN.CEVAE performs worse on TE and CE; the paper attributes this to correlated information retained in its counterfactual prediction.Source: Causal Estimation and Fairness Task · p. 6, Figure 4 · p. 6
Image Generation Task
- For CelebA, the image-generation task flips Mustache or Smiling as the intervention attribute to create counterfactual images.The reported visual comparison includes real images and counterfactuals for Mustache.Source: Image Generation Task · p. 6, Figure 5 · p. 7
Generated Counterfactual Images
- DCEVAE counterfactuals preserve real-image identity apart from the intervention, whereas CVAE alters gender, CEVAE produces blurry images, and mCEVAE fails on some cases.The paper excludes GAN-based methods from this image comparison because they cannot generate a counterfactual matched to a given real-world image.Source: Generated Counterfactual Images · pp. 6–7, Figure 5 · p. 7
Quantitative Analysis on Image Generation Task
- DCEVAE has the highest attribute-classification accuracies and identity-preserving scores, and the lowest FID, among the compared models.The Mustache-generation evaluation reports similar target-attribute classification accuracy for CEVAE, mCEVAE, and DCEVAE.Source: Table 2 · p. 7, Quantitative Analysis on Image… · p. 7
Conclusion
DCEVAE separates exogenous uncertainty into two latent variables and reports causal-effect estimation without a complete graph. Its fair-classification and image-generation applications show strong quantitative performance using counterfactuals matched to real instances.
- DCEVAE separates exogenous uncertainty into intervention-independent ud and intervention-correlated, non-causal ur.Source: Conclusion · p. 7
- The model estimates total and counterfactual effects without requiring a complete causal graph.Source: Conclusion · p. 7
- The fair-classification and counterfactual-generation applications report the best quantitative performance using counterfactual instances matched to real-world examples.Source: Conclusion · p. 7
Ethical Impact
AI screening and recommendation systems are widely used and raise fairness concerns, particularly for people with minority backgrounds. The paper frames counterfactual generation and latent disentanglement as ways to consider altered-background scenarios, while accepting accuracy limits only when damage is minimal and the scenario is acceptable under that altered background.
- AI screening and recommendation systems are used at scale and are prone to fairness concerns, particularly for people with minority backgrounds.Source: Ethical Impact · p. 8
- The paper frames counterfactual generation as a way to examine whether classifications are acceptable under an altered background.Source: Ethical Impact · p. 8
- Accuracy limits are acceptable only when performance damage is controlled and minimal and the result is acceptable under the altered-background scenario.Source: Ethical Impact · p. 8