Counterfactual Generative Modeling with Variational Causal Inference (2410.12730v3)

Abstract: Estimating an individual's counterfactual outcomes under interventions is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, facial images) and covariates are relatively limited. In this case, to predict one's outcomes under counterfactual treatments, it is crucial to leverage individual information contained in the observed outcome in addition to the covariates. Prior works using variational inference in counterfactual generative modeling have been focusing on neural adaptations and model variants within the conditional variational autoencoder formulation, which we argue is fundamentally ill-suited to the notion of counterfactual in causal inference. In this work, we present a novel variational Bayesian causal inference framework and its theoretical backings to properly handle counterfactual generative modeling tasks, through which we are able to conduct counterfactual supervision end-to-end during training without any counterfactual samples, and encourage disentangled exogenous noise abduction that aids the correct identification of causal effect in counterfactual generations. In experiments, we demonstrate the advantage of our framework compared to state-of-the-art models in counterfactual generative modeling on multiple benchmarks.

• The paper introduces a VCI framework that directly optimizes individual-level likelihood for accurate counterfactual outcome prediction.
• It employs a semi-autoencoding loss with adversarial training to effectively disentangle latent features from treatment effects.
• Experimental results on datasets like Morpho-MNIST and CelebA-HQ show VCI's robust performance and superior estimation capabilities.

Counterfactual Generative Modeling with Variational Causal Inference

This paper introduces a novel framework for counterfactual generative modeling called Variational Causal Inference (VCI), addressing a crucial gap in traditional causal inference and generative modeling methods. The focus is on individual-level outcome prediction in high-dimensional scenarios, where outcomes like gene expressions or facial images are significantly higher in dimensionality than the covariates. This presents a challenging landscape for conventional models that typically rely on low-dimensional covariates and factual treatments.

Key Contributions and Methodology

The authors extend beyond previous VAE-based or conditional VAE frameworks that inadequately handle counterfactuals due to their marginal-level likelihood optimization objectives. Instead, they propose a formulation that directly optimizes the individual-level likelihood $p(Y'|Y, X, T, T')$, where $Y'$ represents the counterfactual outcomes. This approach permits end-to-end counterfactual supervision during training, a first in counterfactual generative modeling.

1. Variational Causal Inference Framework: The paper presents a variational lower bound formulation for counterfactual outcomes, derived using Bayesian causal models. The central contribution is in replacing traditional VAE objectives with a theoretically backed framework that incorporates counterfactual variables directly, allowing the disentanglement of latent representations from treatment effects.
2. Optimization Scheme: VCI maintains individuality and treatment specificity throughout the counterfactual generation process by employing a semi-autoencoding loss function supplemented with an adversarial training approach. The divergence term encourages the disentanglement of individual features from treatment characteristics.
3. Robust Estimation Scheme: The framework extends to robustly estimate high-dimensional marginal causal effects, producing asymptotically efficient marginal estimates even in the context of no available counterfactual samples.

Experimental Evaluation

The VCI framework is evaluated on diverse datasets ranging from single-cell perturbation data to image datasets like Morpho-MNIST and CelebA-HQ. The results consistently demonstrate superior performance over existing state-of-the-art models.

• Numerical Results: In single-cell perturbation datasets, the model achieves higher R$^2$ values for out-of-distribution predictions, particularly for differentially-expressed genes. For Morpho-MNIST, VCI shows significant improvements in mean squared error when counterfactual truths are available, showcasing the framework's effectiveness in maintaining both individuality and treatment effect.
• Qualitative Assessment: For facial images in CelebA-HQ, VCI effectively manages to add or remove attributes (like glasses and smiling) while maintaining credible counterfactual constructions. This underscores the system's ability to disentangle latent factors, a task at which prior diffusion models have struggled.

Implications and Future Directions

VCI provides a robust foundation for counterfactual generative modeling, especially in high-dimensional spaces where traditional methods falter. Its ability to facilitate accurate counterfactual predictions without the need for observed counterfactuals holds promise for applications in personalized medicine, policy modeling, and more sensitive attribution tasks in machine learning. Future work could explore integrating causal relations among multiple treatments and extending the framework to non-standard causal assumptions, such as scenarios with unobserved confounders.

In conclusion, this paper advances the methodology for counterfactual inference in high-dimensional contexts, emphasizing a tighter integration of causal modeling principles with variational inference frameworks. The introduction of VCI sets a novel standard by rigorously addressing the shortcomings of existing methods, particularly for tasks necessitating high fidelity in outcome predictions across varying counterfactual conditions.