Estimating Categorical Counterfactuals via Deep Twin Networks (2109.01904v6)

Abstract: Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot be uniquely determined from observations and interventions alone. This raises the question of how to choose the causal mechanisms so that resulting counterfactual inference is trustworthy in a given domain. This question has been addressed in causal models with binary variables, but the case of categorical variables remains unanswered. We address this challenge by introducing for causal models with categorical variables the notion of counterfactual ordering, a principle that posits desirable properties causal mechanisms should posses, and prove that it is equivalent to specific functional constraints on the causal mechanisms. To learn causal mechanisms satisfying these constraints, and perform counterfactual inference with them, we introduce deep twin networks. These are deep neural networks that, when trained, are capable of twin network counterfactual inference -- an alternative to the abduction, action, & prediction method. We empirically test our approach on diverse real-world and semi-synthetic data from medicine, epidemiology, and finance, reporting accurate estimation of counterfactual probabilities while demonstrating the issues that arise with counterfactual reasoning when counterfactual ordering is not enforced.

• The paper introduces Deep Twin Networks (DTNs) that enforce counterfactual ordering and monotonicity to reliably estimate counterfactuals for categorical variables.
• The methodology integrates twin network architectures with deep learning, streamlining counterfactual inference beyond traditional abduction-action-prediction procedures.
• Empirical results on synthetic and real-world datasets, including finance and healthcare, demonstrate DTNs' improved accuracy over conventional methods.

Estimating Categorical Counterfactuals via Deep Twin Networks

The paper "Estimating Categorical Counterfactuals via Deep Twin Networks" addresses a significant challenge in causal inference, particularly for models dealing with categorical variables. While counterfactual inference is a critical tool in various sectors like medicine and finance, existing models primarily focus on binary variables, leaving categorical variable inference underexplored. This paper proposes novel methodologies for reliable counterfactual inference within causal models that involve categorical variables.

Overview of Methodology

The authors introduce the concept of "counterfactual ordering," a principle suggesting that causal mechanisms should exhibit intuitive properties to ensure trustworthiness in a given domain. Counterfactual ordering is mathematically equivalent to imposing specific functional constraints on causal mechanisms, notably monotonicity in the relationship between variables. The work demonstrates that enforcing these constraints helps avoid non-intuitive counterfactual inferences, thus aligning the model's output with domain knowledge.

To effectively learn these causal mechanisms and perform counterfactual inference, the authors develop a framework called Deep Twin Networks (DTNs). DTNs leverage the structure of twin networks alongside deep learning capabilities to estimate counterfactuals more efficiently than traditional methods, such as the abduction-action-prediction approach. Notably, DTNs provide an alternative methodology that simplifies the complex procedures typically required for counterfactual reasoning.

Empirical Evaluation

The effectiveness of the proposed framework is demonstrated through extensive experiments spanning synthetic, semi-synthetic, and real-world datasets from domains such as finance and healthcare. In each scenario, the paper showcases DTNs' ability to produce accurate estimations of counterfactual probabilities and highlights the discrepancies that arise when counterfactual ordering is not enforced. Real-world implementation includes predictively assessing credit risk scenarios in financial datasets and understanding patient outcomes in clinical trial data.

Moreover, on datasets where ground truth is known, DTNs exhibit a strong performance in estimating counterfactuals and the probabilities of causation, directly comparing with theoretical benchmarks and outperforming older methodologies in specific contexts.

Implications and Future Research

Practically, this paper provides a robust framework for implementing counterfactual reasoning in data-driven causal settings with categorical variables. Theoretically, it advances the literature on causal inference by contributing a new understanding of how functional constraints like monotonicity can guide the learning of causal models that provide more reliable outputs.

This work offers several pathways for future exploration. There is potential in extending the DTN framework to accommodate higher-dimensional causal models and more complex causal structures. Further paper could also evaluate the utility of DTNs in other high-stakes domains like autonomous systems and personalized education, where reliable counterfactual inference could significantly influence decision-making processes.

In summary, "Estimating Categorical Counterfactuals via Deep Twin Networks" provides valuable insights and a powerful toolset for enhancing the accuracy and reliability of counterfactual inference in categorical causal models, marking a substantial contribution to both the theoretical and practical facets of causal machine learning.