While prior federated learning (FL) methods mainly consider client heterogeneity, we focus on the *Federated Domain Generalization (DG)* task, which introduces train-test heterogeneity in the FL context. Existing evaluations in this field are limited in terms of the scale of the clients and dataset diversity. Thus, we propose a Federated DG benchmark that aim to test the limits of current methods with high client heterogeneity, large numbers of clients, and diverse datasets. Towards this objective, we introduce a novel data partition method that allows us to distribute any domain dataset among few or many clients while controlling client heterogeneity. We then introduce and apply our methodology to evaluate 14 DG methods, which include centralized DG methods adapted to the FL context, FL methods that handle client heterogeneity, and methods designed specifically for Federated DG on 7 datasets. Our results suggest that, despite some progress, significant performance gaps remain in Federated DG, especially when evaluating with a large number of clients, high client heterogeneity, or more realistic datasets. Furthermore, our extendable benchmark code will be publicly released to aid in benchmarking future Federated DG approaches.

Answering counterfactual queries has important applications such as explainability, robustness, and fairness but is challenging when the causal variables are unobserved and the observations are non-linear mixtures of these latent variables, such as pixels in images. One approach is to recover the latent Structural Causal Model (SCM), which may be infeasible in practice due to requiring strong assumptions, e.g., linearity of the causal mechanisms or perfect atomic interventions. Meanwhile, more practical ML-based approaches using naive domain translation models to generate counterfactual samples lack theoretical grounding and may construct invalid counterfactuals. In this work, we strive to strike a balance between practicality and theoretical guarantees by analyzing a specific type of causal query called *domain counterfactuals*, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). We show that recovering the latent SCM is unnecessary for estimating domain counterfactuals, thereby sidestepping some of the theoretic challenges. By assuming invertibility and sparsity of intervention, we prove domain counterfactual estimation error can be bounded by a data fit term and intervention sparsity term. Building upon our theoretical results, we develop a theoretically grounded practical algorithm that simplifies the modeling process to generative model estimation under autoregressive and shared parameter constraints that enforce intervention sparsity. Finally, we show an improvement in counterfactual estimation over baseline methods through extensive simulated and image-based experiments.

In high-stakes domains such as healthcare and hiring, the role of machine learning (ML) in decision-making raises significant fairness concerns. This work focuses on Counterfactual Fairness (CF), which posits that an ML model's outcome on any individual should remain unchanged if they had belonged to a different demographic group. Previous works have proposed methods that guarantee CF. Notwithstanding, their effects on the model's predictive performance remain largely unclear. To fill this gap, we provide a theoretical study on the inherent trade-off between CF and predictive performance in a model-agnostic manner. We first propose a simple but effective method to cast an optimal but potentially unfair predictor into a fair one with a minimal loss of performance. By analyzing the excess risk incurred by perfect CF, we quantify this inherent trade-off. Further analysis on our method's performance with access to only incomplete causal knowledge is also conducted. Built upon this, we propose a practical algorithm that can be applied in such scenarios. Experiments on both synthetic and semi-synthetic datasets demonstrate the validity of our analysis and methods.