CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training (1709.02023v2)

Abstract: We propose an adversarial training procedure for learning a causal implicit generative model for a given causal graph. We show that adversarial training can be used to learn a generative model with true observational and interventional distributions if the generator architecture is consistent with the given causal graph. We consider the application of generating faces based on given binary labels where the dependency structure between the labels is preserved with a causal graph. This problem can be seen as learning a causal implicit generative model for the image and labels. We devise a two-stage procedure for this problem. First we train a causal implicit generative model over binary labels using a neural network consistent with a causal graph as the generator. We empirically show that WassersteinGAN can be used to output discrete labels. Later, we propose two new conditional GAN architectures, which we call CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained causal implicit generative model for the labels is then a causal implicit generative model over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset.

• The paper introduces Causal Implicit Generative Models that sample from both observational and interventional distributions by structuring the generator with causal graphs.
• It leverages an adversarial training scheme that enforces causal structure, ensuring high label-consistency and accurate conditional sampling.
• Empirical results demonstrate high-quality image synthesis even under unseen label combinations, highlighting the model's robust extrapolation capabilities.

An Overview of CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training

The paper "CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training" explores the intersection of causality and generative models, proposing a framework to integrate causal reasoning into generative adversarial networks (GANs). This approach leverages causal graphs to enhance GANs' ability to sample not just from observational distributions but also from interventional distributions, aligning with the principles of causality.

Core Contributions

1. Causal Implicit Generative Models (CiGM): The authors introduce CiGMs, which allow for sampling from both observational and interventional distributions. These models are crafted by structuring generator architectures according to causal graphs, thereby embedding causal relationships directly into the model design.
2. Adversarial Training with Causal Structure: The paper presents an adversarial training procedure that ensures the generator network adheres to a prescribed causal graph. This structural compliance is posited to enable accurate sampling from conditional and interventional distributions.
3. Conditional and Interventional Sampling: The paper articulates procedures for realizing conditional and interventional sampling using GANs, particularly focusing on generating images contingent on structured label data. The proposed CausalGAN and CausalBEGAN architectures are pivotal in this context, designed to respect both label interdependencies and causal effects.
4. Theoretical Guarantees: A notable theoretical result is the proof that under optimal conditions, the generator produces samples congruent with the class-conditional distributions. This insight extends the typical GAN framework, providing a more robust generative model informed by causal relationships.

Numerical Results

Empirical evaluations underscore the framework's capability to capture both observational and interventional image-label distributions. The results demonstrate the generation of high-quality, label-consistent images even under previously unseen combinations, such as generating images of women with mustaches. This reflects the model's ability to extrapolate beyond the training data, a significant step in enhancing GANs' applicability.

Implications for Research and Practice

The integration of causality into GAN architectures, as introduced by CausalGAN, presents several intriguing avenues for future research and application:

• Enhanced Image Synthesis: The approach could improve the coherence and quality of generated images by adhering more closely to real-world causal dependencies.
• Broader Applicability: Beyond image synthesis, the framework may be applied across other domains where understanding and manipulating causal relationships are crucial, such as healthcare or economics.
• Robustness to Distribution Shifts: The utilization of causal models might increase generative models' robustness to distribution shifts, providing an additional layer of resilience where typical GANs might falter.

Conclusion

The paper's treatment of GANs through a causal lens yields promising advancements in generative modeling. By structuring the generator according to a causal graph, CausalGAN presents a sophisticated mechanism for generating data that respects and utilizes causal dependencies. This work not only addresses a significant challenge in generative modeling but also lays a foundation for further explorations into causally-informed machine learning models. Researchers in AI and machine learning stand to gain from the insights and methodologies presented, potentially leading to more powerful and generalizable generative models in the future.