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Causal inference typically assumes centralized access to individual-level data. Yet, in practice, data are often decentralized across multiple sites, making centralization infeasible due to privacy, logistical, or legal constraints. We address this problem by estimating the Average Treatment Effect (ATE) from decentralized observational data via a Federated Learning (FL) approach, allowing inference through the exchange of aggregate statistics rather than individual-level data. We propose a novel method to estimate propensity scores via a federated weighted average of local scores using Membership Weights (MW), defined as probabilities of site membership conditional on covariates. MW can be flexibly estimated with parametric or non-parametric classification models using standard FL algorithms. The resulting propensity scores are used to construct Federated Inverse Propensity Weighting (Fed-IPW) and Augmented IPW (Fed-AIPW) estimators. In contrast to meta-analysis methods, which fail when any site violates positivity, our approach exploits heterogeneity in treatment assignment across sites to improve overlap. We show that Fed-IPW and Fed-AIPW perform well under site-level heterogeneity in sample sizes, treatment mechanisms, and covariate distributions. Theoretical analysis and experiments on simulated and real-world data demonstrate clear advantages over meta-analysis and related approaches.

Existing fair multi-view clustering methods typically suffer from a severe trade-off between clustering utility and fairness, while incurring prohibitive quadratic complexity on large-scale datasets. To address these challenges, we propose Causal Disentangled Anchor Learning (CDAL), a novel framework that achieves scalable fairness via structural disentanglement. Guided by a structural causal model perspective, CDAL utilizes a dual-anchor mechanism to structurally separate latent representations into orthogonal semantic and sensitive subspaces. We further ensure statistical independence through a linearized Hilbert-Schmidt Independence Criterion (HSIC) constraint, which is optimized via an efficient alternating scheme. Theoretically, we prove the identifiability of the disentangled factors and guarantee the algorithm's global convergence and linear time complexity $\mathcal{O}(n)$. Extensive experiments on large-scale benchmarks demonstrate that CDAL outperforms state-of-the-art methods, achieving a superior utility-fairness trade-off. Our code is publicly available at https://github.com/Tracesource/CDAL.

Multi-task learning (MTL) aims to construct a joint model for multiple tasks by sharing a common representation across domains. To achieve this goal, existing optimization-centric methods either balance task gradients or modify the shared architecture. However, as these approaches remain agnostic to the content of the shared representation, they fail to disentangle task-relevant structure from spurious context, leading to negative transfer and poor generalization. To overcome this limitation, we propose Causal Orthogonal Representations for Multi-Task Learning (CORE-MTL) , a representation-centric framework that structurally disentangles the shared representation into semantic and residual streams, concentrating task-relevant structure in the semantic stream while relegating nuisance variation to the residual stream. We instantiate this framework in the visual domain by leveraging physical priors for structured scenes and statistical constraints for attributes. Theoretically, our method enjoys a tighter out-of-distribution generalization bound than optimization-centric methods and reduces task gradient interference without explicit gradient projection or reweighting. Empirically, CORE-MTL consistently outperforms existing methods on visual multi-task benchmarks in both in-distribution and out-of-distribution settings.

Counterfactual generation aims to simulate realistic hypothetical outcomes under causal interventions. Diffusion models have emerged as a powerful tool for this task, combining DDIM inversion with conditional generation and classifier-free guidance (CFG). In this work, we identify a key limitation of CFG for counterfactual generation: it prescribes a global guidance scale for all attributes, leading to significant spurious changes in inferred counterfactuals. To mitigate this, we propose *Factored Classifier-Free Guidance* (FCFG), a flexible and model-agnostic guidance technique that enables attribute-wise control following a causal graph. FCFG complements recent advances in classifier-free guidance and can be seamlessly extended to advanced guidance schemes such as CFG++ and APG. Our experiments demonstrate that FCFG significantly improves the axiomatic soundness of inferred counterfactuals across both natural and medical image datasets, mitigating spurious amplification effects, and enhancing counterfactual reversibility.

Estimating Heterogeneous Treatment Effects (HTE) from observational data is essential in fields such as healthcare and policy-making, where randomized experiments are often impractical. While representation learning-based methods have shown promise, recent studies suggest that tree-based approaches may offer superior performance on tabular data, particularly in the presence of uninformative features. We introduce **GRA**dient-based **C**ausal tree **E**nsembles (GRACE), a novel tree-based architecture for HTE estimation that incorporates multi-way, oblique, and soft splits, enabling end-to-end training via backpropagation. GRACE can be seamlessly integrated into existing models as a replacement for fully-connected neural network layers. Across diverse benchmarks involving binary and non-binary treatment settings, GRACE consistently surpasses neural network and tree-based baselines, often by a substantial margin. We further analyze GRACE as an extension of fully-connected neural network layers and conduct ablation studies to isolate and quantify the contribution of each architectural component to the improvement in performance. These results position GRACE as a promising new foundation for flexible, robust, and accurate HTE estimation. GRACE code is available at https://github.com/ysk-kano/GRACE

Efficiently scaling Large Language Models (LLMs) necessitates exploring alternatives to dominant autoregressive (AR) methods, with Masked Diffusion Models (MDMs) emerging as candidates. However, comparing AR (typically decoder-only) and MDM (often encoder-only) paradigms is confounded by differing architectures, obscuring true algorithmic and efficiency trade-offs. This research decouples these factors by evaluating MDMs within a decoder-only framework to: (1) Equitably compare MDM (as Any-Order AR) and standard AR paradigms through discrepancies on orders. (2) Investigate MDM architectural impacts on computational efficiency. We show decoder-only MDMs, despite a larger modeling space, can achieve significant inference speedups ($\sim25\times$) and comparable perplexity with techniques like temperature annealing, offering a path to reduced inference compute. This work provides insights for developing more computationally efficient foundation models by disentangling core modeling choices from architectural influences. Code is available at \url{https://github.com/scxue/AO-GPT-MDM}.

Estimating Individual Treatment Effects (ITE) in multi-treatment scenarios faces two critical challenges: the Hyperparameter Selection Dilemma for balancing weights and the Curse of Dimensionality in computational scalability. This paper derives a novel multi-treatment generalization bound and proposes a theoretical estimator for the optimal balancing weight $\alpha$, eliminating expensive heuristic tuning. We investigate three balancing strategies: Pairwise, One-vs-All (OVA), and Treatment Aggregation. While OVA achieves superior precision in low-dimensional settings, our proposed Treatment Aggregation ensures both accuracy and $\mathcal{O}(1)$ scalability as the treatment space expands. Furthermore, we extend our framework to a generative architecture, Multi-Treatment CausalEGM, which preserves the Wasserstein geodesic structure of the treatment manifold. Experiments on semi-synthetic and image datasets demonstrate that our approach significantly outperforms traditional models in estimation accuracy and efficiency, particularly in large-scale intervention scenarios.

Negative sampling is an important yet challenging component in self-supervised graph representation learning, particularly for recommendation systems where user-item interactions are modeled as bipartite graphs. Existing methods often rely on heuristics or human-specified principles to design negative sampling distributions. This potentially overlooks the usage of an underlying ``true'' negative distribution, which we might be able to access as an oracle despite not knowing its exact form. In this work, we shift the focus from manually designing negative sampling distributions to a more principled method that approximates and leverages the underlying true distribution from the ground up. We expand this idea in the analysis of two scenarios: (1) when the observed graph is an unbiased sample from the true distribution, and (2) when the observed graph is biased with partially observable positive edges. The analysis result is the derivation of a sampling strategy as the numerical approximation of a well-established learning objective. Our theoretical findings are also empirically validated, and our new sampling methods achieve state-of-the-art performance on real-world datasets.

Foundation models based on prior-data fitted networks (PFNs) have shown strong empirical performance in causal inference by framing the task as an in-context learning problem. However, it is unclear whether PFN-based causal estimators provide uncertainty quantification that is consistent with classical frequentist estimators. In this work, we address this gap by analyzing the frequentist consistency of PFN-based estimators for the average treatment effect (ATE). (1) We show that existing PFNs, when interpreted as Bayesian ATE estimators, can exhibit prior-induced confounding bias: the prior is not asymptotically overwritten by data, which, in turn, prevents frequentist consistency. (2) As a remedy, we suggest employing a calibration procedure based on a one-step posterior correction (OSPC). We show that the OSPC helps to restore frequentist consistency and can yield a semi-parametric Bernstein-von Mises theorem for calibrated PFNs (i.e., both the calibrated PFN-based estimators and the classical semi-parametric efficient estimators converge in distribution with growing data size). (3) Finally, we implement OSPC through tailoring martingale posteriors on top of the PFNs. In this way, we are able to recover functional nuisance posteriors from PFNs, required by the OSPC. In multiple (semi-)synthetic experiments, PFNs calibrated with our martingale posterior OSPC produce ATE uncertainty that (i) asymptotically matches frequentist uncertainty and (ii) is well calibrated in finite samples in comparison to other Bayesian ATE estimators.

Causal Abstraction (CA) theory provides a principled framework for relating causal models that describe the same system at different levels of granularity while ensuring interventional consistency between them. Recent methods for learning CAs, however, assume fixed and well-specified exogenous distributions, leaving them vulnerable to environmental shifts and model misspecification. In this work, we address these limitations by introducing the first class of distributionally robust CAs and their associated learning algorithms. The latter cast robust causal abstraction learning as a constrained min-max optimization problem with Wasserstein ambiguity sets. We provide theoretical guarantees for both empirical and Gaussian environments, enabling principled selection of ambiguity-set radii and establish quantitative guarantees on worst-case abstraction error. Furthermore, we present empirical evidence across different problems and CA learning methods, demonstrating our framework’s robustness not only to environmental shifts but also to structural and intervention mapping misspecification.

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism is the most effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Counterfactual reasoning is one of the fundamental facets of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. It describes the queries what would have happened had some intervention been performed given that something else, corresponding to Layer 3 of the Pearl Causal Hierarchy. In this project, we examine a specific type of counterfactual quantities, called counterfactual direct (Ctf-DE), indirect (Ctf-IE), and spurious (Ctf-SE) effects for quantifying fairness in a sequential decision-making framework. Building on these measures, we formulate an online causally-fair learning problem with multiple long-term constraints and study it in both non-parametric contextual bandits and parametric logistic bandits settings. We achieve sublinear regret and violations bounds for both bandits settings with roundwise counterfactual fairness constraints (that are a priori unknown) without Slater's condition. For logistic bandits, our method achieves $\mathcal{O}(1)$ per-round time complexity using an online mirror descent estimator, yielding an efficient algorithm.

Previous work establishing completeness results for *counterfactual identification* has been limited to the setting where the input data belongs to observational and interventional distributions (Layers 1 and 2 of Pearl's Causal Hierarchy), since it was generally presumed impossible to obtain data from counterfactual distributions, belonging to Layer 3. However, recent work (Raghavan & Bareinboim, 2025) has formally characterized a family of counterfactual distributions which can be directly estimated via experimental methods - a notion they call *counterfactual realizabilty*. This leaves open the question of what *additional* Layer 3 quantities now become identifiable, given this new access to (some) Layer 3 data. We develop the **ctfIDu+** algorithm for identifying a counterfactual query from an arbitrary set of Layer 3 data, and prove that it is complete for this task. Using this, we establish the theoretical limit of which counterfactuals can be identified from physically realizable data, thus implying the *fundamental limit to exact causal inference in the non-parametric setting*. Finally, we derive novel analytic bounds for important non-identifiable quantities given realizable counterfactual data, that are provably tighter than the previously established benchmark. We corroborate using simulations that even if a quantity is non-identifiable, counterfactual data can be used to further tighten bounds for its range.

Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

In many applications, practical constraints prevent measuring covariates and outcomes on the same units, resulting in unpaired data. We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates $X$ and an outcome $Y$ under different experimental conditions (environments) but do not observe them jointly -- we either observe $X$ or $Y$. Under appropriate regularity conditions, the problem can be cast as an instrumental variable (IV) regression with the environment acting as a (possibly high-dimensional) instrument. When there are many environments but only a few observations per environment, standard two-sample IV estimators fail to be consistent. We propose a GMM-type estimator based on cross-fold sample splitting of the instrument–covariate sample that also applies in standard IV settings. We prove that it is consistent as the number of environments grows but the sample size per environment remains constant. We further extend the method to sparse causal effects via $\ell_1$-regularized estimation and post-selection refitting.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: *interference reveals structure* in the latent confounder. Leveraging this insight, we propose the **Spatial Deconfounder**, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions—without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Identifying the drivers of causal mechanism shifts, distinguishing functional changes from noise alterations, termed *dissection*, is a critical yet under-explored problem in data science (e.g., biomedical science and manufacturing). This paper introduces a more general and unified framework, the *function and noise separation* (FANS) framework, that detects and dissects shifts in non-additive, non-linear Structural Causal Models (SCMs) beyond existing additive noise models. Our approach is grounded in a theoretical independence criterion, where function shifts induce a statistical dependence between a node's parents and residual noise. Building on this foundation, we develop a practical two-stage algorithm to efficiently detect and dissect these shifts without retraining. Furthermore, we address the complex challenge of simultaneous function and noise shifts, introducing a formal assumption to resolve their inherent non-identifiability. Our results are corroborated by simulations. Our code is available at https://github.com/MLAI-Yonsei/FANS/.

For many real-world systems, causal ground truth is difficult to obtain, making claims about causal effects hard to assess. We develop methods for evaluating collections of bivariate causal statements, one for each pair of variables in a fixed system. In the setting of acyclic linear statements, any such collection can be extended to a unique multivariate causal model, but we argue that this induced model is implausible if it imposes substantial additional confounding to explain observed correlations. We introduce a compatibility score that quantifies this notion of plausibility, notably without relying on the faithfulness assumption. Additionally, we define an incompatibility score for purely graphical bivariate causal statements, based on global consistency constraints that are derived from acyclicity and faithfulness assumptions. We give theoretical and empirical evidence that both scores can successfully distinguish correct from incorrect causal statements in generic settings. Moreover, we demonstrate the practical applicability of our methods by analyzing causal claims made by large language models. Our work aims to provide a foundation for assessing the reliability of causal information derived from human experts or artificial intelligence in settings where alternative forms of validation are unavailable.

Fairness in machine learning prediction has attracted growing attention in recent years. In this article, we propose a causal–inference–based framework for fair prediction, defined through path-specific counterfactual interventions. Instead of imposing fairness via constraints on predictive objectives or model parameters, our approach specifies fairness directly at the level of counterfactual prediction semantics. Given a learned causal graph, we construct a predictive distribution for the outcome $Y$ using a structural causal model and generate counterfactual predictions by selectively intervening on causal paths emanating from sensitive attributes. By allowing or blocking the propagation of sensitive information along designated paths, possibly involving multiple sensitive sources, our framework induces a hierarchy of interpretable fairness notions, generalizing standard path-specific causal semantics. Our empirical experiments demonstrate how different fairness levels can be instantiated and compared in practice.

Amortized causal inference via Prior-data Fitted Networks (PFNs) has emerged as a promising paradigm, enabling zero-shot estimation of causal effects without the need for dataset-specific model tuning. However, the principled effectiveness of unified pre-training across general interventional regimes remains an underexplored question. In this paper, we investigate interventions on subsets of variables within Structural Causal Models (SCMs) and identify a fundamental theoretical limitation of current pre-training approaches. Theoretically, we prove that a single observational SCM induces an exponentially large space of interventional distributions, resulting in a phenomenon we term prior uncoverage. Consequently, this uncoverage yields a mismatch between the learned meta-prior and the true grounding prior, leading to unavoidable posterior inconsistency and estimation bias. To address this, we posit that fine-tuning is a fundamental necessity and propose a target-specific strategy named Point-Wise Interventional Fine-tuning (PWF), enabling the local generalization property. We further scale this approach via Meta-Sampling Fine-tuning (MSF) from a budgeted active learning perspective, thereby achieving uniform generalization on any interventional distribution.