深度学习 · causal inference

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.

Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most of the existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) that the intervention targets for the data generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework to learn nonlinear causal cyclic relationships from soft interventional data with unknown targets. Our main approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures—contractive residual flows and neural spline flows. By conducting experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph and unknown target recovery across various interventional and noise settings.

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.

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.

We propose causal preference elicitation, a Bayesian framework for expert-in-the-loop causal discovery that actively queries local edge relations to concentrate a posterior over directed acyclic graphs (DAGs). From any black-box observational posterior, we model noisy expert judgments with a three-way likelihood over edge existence and direction. Posterior inference uses a flexible particle approximation, and queries are selected by an efficient expected information gain criterion on the expert’s categorical response. Experiments on synthetic graphs, protein signaling data, and a human gene perturbation benchmark show faster posterior concentration and improved recovery of directed effects under tight query budgets.

Extracting causally meaningful features from time-series data is fundamental for robust machine learning under distribution shifts. In process monitoring, existing methods struggle to maintain detection performance when operating conditions change. Current approaches capture either temporal causal relationships or cross-environment invariance, but not both simultaneously. We propose Causal Feature Learning (CFL), a unified framework that jointly optimizes for temporal relevance and environment mean invariance. CFL formulates feature extraction as a generalized Rayleigh-quotient problem, maximizing correlation with target variables while penalizing sensitivity to environment-dependent mean shifts. Theoretical analysis establishes conditions under which CFL identifies a mean-invariant predictive subspace. Experiments on the Tennessee Eastman Process demonstrate that CFL achieves 93.69\% average fault detection rate, outperforming 15 baseline methods and validating the benefit of jointly capturing both aspects of causality.

The scalability of Large Language Models to long sequences is hindered by the quadratic cost of self-attention and the limitations of positional encodings. To address these, we introduce **Caracal**, a novel architecture that replaces self-attention with a parameter-efficient, $\mathcal{O}(L \log L)$ Multi-Head Fourier (MHF) module. Our contributions are threefold: (1) We leverage the Fast Fourier Transform (FFT) for sequence mixing, inherently addressing both bottlenecks mentioned above. (2) We apply a frequency-domain causal masking technique that enforces autoregressive capabilities via asymmetric padding and truncation, overcoming a critical barrier for Fourier-based generative models. (3) Unlike efficient models relying on hardware-specific implementations (e.g., Mamba), **Caracal** uses standard library operators. This ensures robust portability, eliminating common deployment barriers. Evaluations demonstrate that **Caracal** performs competitively with Transformer and SSM baselines, offering a scalable and simple pathway for efficient long-sequence modeling. Code is available in the supplementary materials.

In standard causal attention, each token's query, key, and value (QKV) are static and encode only preceding context. We introduce CAuSal aTtention with Lookahead kEys (CASTLE), an attention mechanism that continually updates each token's keys as the context unfolds. We term these updated keys lookahead keys because they belong to earlier positions yet integrate information from tokens that appear later relative to those positions, while strictly preserving the autoregressive property. Although the mechanism appears sequential, we derive a mathematical equivalence that avoids explicitly materializing lookahead keys at each position and enables efficient parallel training. On language modeling benchmarks, CASTLE consistently outperforms standard causal attention across model scales, reducing validation perplexity and improving average performance on a range of downstream tasks.

Estimating causal structure in the presence of latent variables is an important yet challenging problem. Recent works have shown that distributional constraints, such as rank deficiency constraints of the covariance matrices, can be exploited to recover the underlying causal structure involving latent variables. However, real-world data often exhibit heterogeneity/nonstationarity, which pose challenges to existing methods. In this work, we develop a principled approach for identifying the structure of partially observed linear causal models from heterogenous/nonstationary data. We first formulate a class of heterogenous/nonstationary, partially observed linear causal models and prove that their distributional constraints are equivalent to those in the homogeneous case. Building on this, we propose a novel rank deficiency test that can efficiently handle heterogenous/nonstationary data, and further establish identifiability results for recovering the causal structure involving latent variables. We also provide a method to identify which variables exhibit distribution shifts, i.e., whose causal mechanisms vary across domains. Experiments on simulated and real-world data validate our theoretical findings and the effectiveness of our method.

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near $0$ and $1$ often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

Synthetic Nearest Neighbors (SNN) provides a principled solution to causal matrix completion under missing-not-at-random (MNAR) by exploiting local low-rank structure through fully observed anchor submatrices. However, its effectiveness critically relies on sufficient data availability within each treatment level, a condition that often fails in settings with multiple or complex treatments. In this work, we propose Mixed Synthetic Nearest Neighbors (MSNN), a new entry-wise causal identification estimator that integrates information across treatment levels. We show that MSNN retains the finite-sample error bounds and asymptotic normality guarantees of SNN, while enlarging the effective sample size available for estimation. Empirical results on synthetic and real-world datasets illustrate the efficacy of the proposed approach, especially under data-scarce treatment levels.

We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual outcome distributions. Unlike classical quantities such as the average treatment effect, it captures differences across entire distributions. We show that this estimand can be written as a smooth transformation of counterfactual mean embeddings with an appropriate kernel. This characterization allows us to establish first-order pathwise differentiability in general, and second-order pathwise differentiability under the null hypothesis of equal counterfactual distributions. Leveraging this smoothness, we construct debiased estimators and asymptotically valid tests for distributional treatment effects at a fixed entropic regularization parameter. Because the power of the test depends on this unknown parameter, we propose an aggregated test that combines evidence across a grid of regularization choices. Experiments on simulated and image data demonstrate the practical advantages of our estimator and testing procedure.

It is a fundamental challenge to ascertain whether the causal effect of a treatment on an outcome is identifiable in the presence of latent confounders, which serves as the logical prerequisite for recovering the causal effect in a partially observed system. While prior literature demonstrates that the causal effect is identifiable when there exist auxiliary variables subject to stringent structural constraints, this paper investigates identifiability of the causal effect without such variables. This means that we ground identifiability solely in the joint distribution of the treatment-outcome pair, which constitutes the irreducible statistical basis for causal effect identification. Focusing on linear structural causal models (SCMs), we provide a nuanced and complete characterization of identifiability of the causal effect contingent on the distributional properties of exogenous noises. Specifically, we formulate a set of mutually exclusive and collectively exhaustive conditions regarding the Gaussianity of exogenous noises, ascertain under which conditions the causal effect is identifiable and under which it is not, while also quantifying the cardinality of the feasible solution set for the unidentifiable cases. Finally, we empirically validate our theoretical findings.

The quadratic computational complexity of self-attention remains a fundamental bottleneck for scaling Large Language Models (LLMs) to long contexts, particularly during the pre-filling phase. In this paper, we rethink the causal attention mechanism from the perspective of information flow. Due to causal constraints, tokens at initial positions participate in the aggregation of every subsequent token. However, existing sparse methods typically apply a uniform top-$k$ selection across all token positions within a layer, ignoring the cumulative dependency of token information inherent in causal architectures. To address this, we propose Stem, a novel, plug-and-play sparsity module aligned with information flow. First, Stem employs the Token Position-Decay strategy, applying position-dependent top-$k$ within each layer to retain initial tokens for recursive dependencies. Second, to preserve information-rich tokens, Stem utilizes the Output-Aware Metric. It prioritizes high-impact tokens based on approximate output magnitude. Extensive evaluations demonstrate that Stem achieves superior accuracy with reduced computation and pre-filling latency. Code is available at https://anonymous.4open.science/r/stem-254ENLXL.

As black box models and pretrained models gain traction in time series applications, understanding and explaining their predictions becomes increasingly vital, especially in high-stakes domains where interpretability and trust are essential. However, most of the existing methods involve only in-distribution explanation, and do not generalize outside the training support, which requires the learning capability of generalization. In this work, we aim to provide a framework to explain black-box models for time series data through the dual lenses of Sparse Autoencoders (SAEs) and causality. We show that many current explanation methods are sensitive to distributional shifts, limiting their effectiveness in real-world scenarios. Building on the concept of Sparse Autoencoder, we introduce TimeSAE, a framework for black-box model explanation. We conduct extensive evaluations of TimeSAE on both synthetic and real-world time series datasets, comparing it to leading baselines. The results, supported by both quantitative metrics and qualitative insights, show that TimeSAE provides more faithful and robust explanations. Our code is available in an easy-to-use library TimeSAE-Lib: https://oublalkhalid.github.io/TimeSAE/

Robotic policies deployed in real-world environments often encounter post-training faults, where retraining, exploration, or system identification are impractical. We introduce an inference-time, cerebellar-inspired residual control framework that augments a frozen reinforcement learning policy with online corrective actions, enabling fault recovery without modifying base policy parameters. The framework instantiates core cerebellar principles, including high-dimensional pattern separation via fixed feature expansion, parallel microzone-style residual pathways, and local error-driven plasticity with excitatory and inhibitory eligibility traces operating at distinct time scales. These mechanisms enable fast, localized correction under post-training disturbances while avoiding destabilizing global policy updates. A conservative, performance-driven meta-adaptation regulates residual gain and plasticity, preserving nominal behavior and suppressing unnecessary intervention. Experiments on MuJoCo benchmarks under actuator, dynamic, and environmental perturbations show improvements of up to $+66$% on $\texttt{HalfCheetah-v5}$ and $+53$% on $\texttt{Humanoid-v5}$ under moderate faults, with graceful degradation under severe shifts and complementary robustness from consolidating persistent residual corrections into policy parameters.

Large Language Models (LLMs) often produce hallucinated outputs, which limit their reliability in high-stakes applications. Conformal prediction can provide guarantees on the correctness and factuality of LLM outputs, but existing approaches rely on the exchangeability assumption, which rarely holds in online settings where user queries and interests change over time. To solve this problem, in this paper, we propose **PACE** (**P**roactive **A**daptive **C**onformal Inferenc**E**), a novel framework that sequentially updates the time-varying target miscoverage parameter with a dynamic step size to maintain valid coverage under online distribution shifts. PACE is motivated by the theoretical connections between expected miscoverage error and key factors such as distribution shifts and instantaneous parameter error. It integrates two complementary signals: (1) a proactive shift detection to estimate the magnitude of distribution shifts, and (2) a reactive error that scales updates according to the local coverage gap. Extensive experiments on synthetic and real-world datasets demonstrate that PACE consistently outperforms advanced adaptive baselines. It reduces the deviation from the target error rate by up to 60\% in QA tasks and accelerates coverage recovery by over 2.5x during abrupt shifts, ensuring stable factuality guarantees without compromising utility and stability.

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to represent. Recovering causal effects from such sub-population is an important problem in causal inference, as estimating average treatment effects (ATE) from selected populations can result in a severely biased estimate of the ATE from the whole population. In this paper, we investigate the identifiability of the ATE under selection bias. We provide *necessary and sufficient conditions* for ATE identifiability, leveraging weak assumptions on probability classes to characterize propensity score and selection probability, which are weaker assumptions than those required by existing general identification frameworks. Compared to previous works, our results extend existing graphical identifiability criteria and offer a more comprehensive understanding of causal effect identification *with strictly weaker conditions* in the presence of selection bias.

Identifying optimal intervention sequences from offline data to guide temporal systems toward target outcomes is a critical challenge with profound implications for fields like personalized medicine. While existing methods are mostly evaluated in offline settings, practical applications demand online, adaptive strategies that can respond in real-time. To address this, we propose \textbf{G}oal-conditioned \textbf{I}ntervention via \textbf{F}actual-\textbf{T}argeted Training (\textbf{GIFT}), a novel framework for learning sequential intervention policies from observational data. GIFT learns a goal-conditioned policy by rescaling rewards with clipped importance weights, stabilizing learning and steering toward the target. Under standard assumptions, the induced operator has a unique fixed point and our procedure converges to it. We also bound the bias from clipping and approximation via the gap to the policy’s true value. Experiments show GIFT significantly outperforms existing methods in creating goal-conditioned policies for online deployment.