The Equalized Odds (for short, EO) is one of the most popular measures of discrimination used in the supervised learning setting. It ascertains fairness through the balance of the misclassification rates (false positive and negative) across the protected groups -- e.g., in the context of law enforcement, an African-American defendant who would not commit a future crime will have an equal opportunity of being released, compared to a non-recidivating Caucasian defendant. Despite this noble goal, it has been acknowledged in the literature that statistical tests based on the EO are oblivious to the underlying causal mechanisms that generated the disparity in the first place (Hardt et al. 2016). This leads to a critical disconnect between statistical measures readable from the data and the meaning of discrimination in the legal system, where compelling evidence that the observed disparity is tied to a specific causal process deemed unfair by society is required to characterize discrimination. The goal of this paper is to develop a principled approach to connect the statistical disparities characterized by the EO and the underlying, elusive, and frequently unobserved, causal mechanisms that generated such inequality. We start by introducing a new family of counterfactual measures that allows one to explain the misclassification disparities in terms of the underlying mechanisms in an arbitrary, non-parametric structural causal model. This will, in turn, allow legal and data analysts to interpret currently deployed classifiers through causal lens, linking the statistical disparities found in the data to the corresponding causal processes. Leveraging the new family of counterfactual measures, we develop a learning procedure to construct a classifier that is statistically efficient, interpretable, and compatible with the basic human intuition of fairness. We demonstrate our results through experiments in both real (COMPAS) and synthetic datasets.

However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side-information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios.

The Equalized Odds (for short, EO) is one of the most popular measures of discrimination used in the supervised learning setting. It ascertains fairness through the balance of the misclassification rates (false positive and negative) across the protected groups -- e.g., in the context of law enforcement, an African-American defendant who would not commit a future crime will have an equal opportunity of being released, compared to a non-recidivating Caucasian defendant. Despite this noble goal, it has been acknowledged in the literature that statistical tests based on the EO are oblivious to the underlying causal mechanisms that generated the disparity in the first place (Hardt et al. 2016). This leads to a critical disconnect between statistical measures readable from the data and the meaning of discrimination in the legal system, where compelling evidence that the observed disparity is tied to a specific causal process deemed unfair by society is required to characterize discrimination. The goal of this paper is to develop a principled approach to connect the statistical disparities characterized by the EO and the underlying, elusive, and frequently unobserved, causal mechanisms that generated such inequality. We start by introducing a new family of counterfactual measures that allows one to explain the misclassification disparities in terms of the underlying mechanisms in an arbitrary, non-parametric structural causal model. This will, in turn, allow legal and data analysts to interpret currently deployed classifiers through causal lens, linking the statistical disparities found in the data to the corresponding causal processes. Leveraging the new family of counterfactual measures, we develop a learning procedure to construct a classifier that is statistically efficient, interpretable, and compatible with the basic human intuition of fairness. We demonstrate our results through experiments in both real (COMPAS) and synthetic datasets.

Long-horizon embodied planning is challenging because the world does not only change through an agent's actions: exogenous processes (e.g., water heating, dominoes cascading) unfold concurrently with the agent's actions. We propose a framework for abstract world models that jointly learns (i) symbolic state representations and (ii) causal processes for both endogenous actions and exogenous mechanisms. Each causal process models the time course of a stochastic cause-effect relation. We learn these world models from limited data via variational Bayesian inference combined with LLM proposals. Across five simulated tabletop robotics environments, the learned models enable fast planning that generalizes to held-out tasks with more objects and more complex goals, outperforming a range of baselines.

However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side-information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios.

To clarify the origins of ASVs, we will modify lines 146-7: "In the game theory literature, this axiom was first relaxed To clarify the notion of accuracy in the global Shapley sum rule, we will add: "The accuracy of randomly drawing from Sec 4.3) could occur at any point in the time series: Each time series We will add a sentence in the text to clarify this and hope this makes the application seem less odd. Regarding R1's concern about the inefficiency of ASVs for feature selection, we propose to reframe Sec 4.4 as Please also see lines 29-32 below in our response to R3. R3's largest concern is that our paper does not discuss the difference between our approach and [19], which appears We will make the following addition to the end of Sec 3.2: Note that this is quite distinct from other work [19], which considers the model's prediction process itself In contrast, ASVs incorporate causal structure present in the data itself." R3 finds ASVs' incorporation of causality to be mainly based on intuition. We will clarify this in our introduction to ASVs. R3 is correct that the ASVs of Sec 4.2 place gender and department choice out-of-causal ordering.