We propose causal effect estimators based on empirical Fr\'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity while preserving robustness to treatment misspecification. Using structural assumptions, we obtain compact representations of potential outcomes, enabling scalable estimation of causal effects over time and across covariates. We provide both theoretical, regarding the consistency of functional causal effects, as well as empirical comparison of a range of proposed causal effect estimators. Applications to binary treatment settings with functional outcomes illustrate the framework's utility in biomedical monitoring, where outcomes exhibit complex temporal dynamics. Our estimators accommodate scenarios with registered covariates and outcomes, aligning them to the Fr\'{e}chet means, as well as cases requiring higher-order representations to capture intricate covariate-outcome interactions. These advancements extend causal inference to dynamic and non-linear domains, offering new tools for understanding complex treatment effects in functional data settings.

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider coarsened exact matching, developed in Iacus et al. (2011). While they developed some statistical properties, in this article, we study the approach using asymptotics based on a superpopulation inferential framework. This methodology is generalized to what we termed as coarsened confounding, for which we propose two new algorithms. We develop asymptotic results for the average causal effect estimator as well as providing conditions for consistency. In addition, we provide an asymptotic justification for the variance formulae in Iacus et al. (2011). A bias correction technique is proposed, and we apply the proposed methodology to data from two well-known observational studies.

In many settings, machine learning models may be used to inform decisions that impact individuals or entities who interact with the model. Such entities, or agents, may game model decisions by manipulating their inputs to the model to obtain better outcomes and maximize some utility. We consider a multi-agent setting where the goal is to identify the "worst offenders:" agents that are gaming most aggressively. However, identifying such agents is difficult without knowledge of their utility function. Thus, we introduce a framework in which each agent's tendency to game is parameterized via a scalar. We show that this gaming parameter is only partially identifiable. By recasting the problem as a causal effect estimation problem where different agents represent different "treatments," we prove that a ranking of all agents by their gaming parameters is identifiable. We present empirical results in a synthetic data study validating the usage of causal effect estimation for gaming detection and show in a case study of diagnosis coding behavior in the U.S. that our approach highlights features associated with gaming.

In many classification datasets, the task labels are spuriously correlated with some input attributes. Classifiers trained on such datasets often rely on these attributes for prediction, especially when the spurious correlation is high, and thus fail to generalize whenever there is a shift in the attributes' correlation at deployment. If we assume that the spurious attributes are known a priori, several methods have been proposed to learn a classifier that is invariant to the specified attributes. However, in real-world data, information about spurious attributes is typically unavailable. Therefore, we propose a method to automatically identify spurious attributes by estimating their causal effect on the label and then use a regularization objective to mitigate the classifier's reliance on them. Compared to a recent method for identifying spurious attributes, we find that our method is more accurate in removing the attribute from the learned model, especially when spurious correlation is high. Specifically, across synthetic, semi-synthetic, and real-world datasets, our method shows significant improvement in a metric used to quantify the dependence of a classifier on spurious attributes ($\Delta$Prob), while obtaining better or similar accuracy. In addition, our method mitigates the reliance on spurious attributes even under noisy estimation of causal effects. To explain the empirical robustness of our method, we create a simple linear classification task with two sets of attributes: causal and spurious. We prove that our method only requires that the ranking of estimated causal effects is correct across attributes to select the correct classifier.

One of the fundamental challenges in causal inference is to estimate the causal effect of a treatment on its outcome of interest from observational data. However, causal effect estimation often suffers from the impacts of confounding bias caused by unmeasured confounders that affect both the treatment and the outcome. The instrumental variable (IV) approach is a powerful way to eliminate the confounding bias from latent confounders. However, the existing IV-based estimators require a nominated IV, and for a conditional IV (CIV) the corresponding conditioning set too, for causal effect estimation. This limits the application of IV-based estimators. In this paper, by leveraging the advantage of disentangled representation learning, we propose a novel method, named DVAE.CIV, for learning and disentangling the representations of CIV and the representations of its conditioning set for causal effect estimations from data with latent confounders. Extensive experimental results on both synthetic and real-world datasets demonstrate the superiority of the proposed DVAE.CIV method against the existing causal effect estimators.

There is a recent trend to leverage the power of graph neural networks (GNNs) for brain-network based psychiatric diagnosis, which, in turn, also motivates an urgent need for psychiatrists to fully understand the decision behavior of the used GNNs. However, most of the existing GNN explainers are either post-hoc in which another interpretive model needs to be created to explain a well-trained GNN, or do not consider the causal relationship between the extracted explanation and the decision, such that the explanation itself contains spurious correlations and suffers from weak faithfulness. In this work, we propose a granger causality-inspired graph neural network (CI-GNN), a built-in interpretable model that is able to identify the most influential subgraph (i.e., functional connectivity within brain regions) that is causally related to the decision (e.g., major depressive disorder patients or healthy controls), without the training of an auxillary interpretive network. CI-GNN learns disentangled subgraph-level representations α and β that encode, respectively, the causal and noncausal aspects of original graph under a graph variational autoencoder framework, regularized by a conditional mutual information (CMI) constraint. We also empirically evaluate the performance of CI-GNN against three baseline GNNs and four state-of-the-art GNN explainers on synthetic data and three largescale brain disease datasets. We observe that CI-GNN achieves the best performance in a wide range of metrics and provides more reliable and concise explanations which have clinical evidence. Introduction Psychiatric disorders have constituted an extensive social and economic burden for health care systems worldwide Wittchen et al. (2011), but the underlying pathological and neural mechanism of the psychiatric disorders still remains uncertain. There are no unified or neuropathological structural traits for psychiatric diagnosis due to the clinical heterogeneity Goodkind et al. (2015); Lanillos et al. (2020). Current diagnosis for psychiatric disorders are mainly based on subjective symptoms and signs Zhang et al. (2021), such as insomnia and anxiety, etc. However, this way for diagnosis has huge limitations in heavily relying on related symptoms and observational status, which could lead to misdiagnosis and delay the early diagnosis and treatment Huang et al. (2020). As a noninvasive neuroimaging technique, the functional magnetic resonance imaging (fMRI) Matthews and Jezzard (2004) has become a popular to investigate neural patterns of brain function for psychiatric disorders Peraza-Goicolea et al. (2020). Using fMRI, extensive studies in psychiatric diagnosis have been conducted to apply functional connectivity (FC) measured with the pairwise correlations of fMRI time series as features to discriminate psychiatric patients and healthy controls, as illustrated in Figure 1a.