Causal Identifiability

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Causal identifiability studies whether observations, interventions, or other information determine a causal graph or quantity uniquely, rather than merely predicting outcomes. Methods include graphical criteria such as do-calculus, structural equation models with assumptions about noise or functional form, and information from proxies, instruments, multiple environments, or targeted interventions. When unique recovery is impossible, partial-identification methods derive bounds, while newer work also examines finite-sample reliability and computational feasibility. A central challenge is that conclusions depend on assumptions and available data: stronger assumptions can make identification possible, but must be justified and tested against alternative models.

Latest papers

128 papers20 papers in the last four weeks, up 54% on the four weeks before. 0.1% of all new papers.

May 8, 2026

Causal EpiNets: Precision-corrected Bounds on Individual Treatment Effects using Epistemic Neural Networks

Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined experimental and observational data. In finite samples, however, standard plug-in estimators systematically fail: they violate structural probability constraints and suffer from extremum bias induced by max-min operators, yielding spuriously narrow intervals. We propose a neural framework for finite-sample PNS estimation that resolves both pathologies. We introduce an anchored neural architecture that guarantees structural constraint satisfaction by construction. To correct extremum bias, we employ precision-corrected intersection-bound inference, leveraging Epistemic Neural Networks for scalable, high-dimensional uncertainty quantification. Empirical evaluations confirm that this approach maintains nominal coverage and exact constraint validity in high-dimensional regimes where standard estimators systematically undercover.

Gandharv Patil, Keyi Tang, Raquel Aoki +1

McGill University/Mila · RBC Borealis

Causal Effect Estimation Causal Identifiability Causal Reasoning Individualized Treatment Effect Estimation

May 7, 2026

Optimal Experiments for Partial Causal Effect Identification

Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.

Tobias Maringgele, Jalal Etesami

Technical University of Munich

Causal Effect Estimation Partial Identification Causal Identifiability Causal Inference Causal Intervention

May 7, 2026

A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs

Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

Alexander G. Reisach, Antoine Chambaz, Gilles Blanchard +1

Laboratoire de Mathématiques d’Orsay Université Paris-Saclay 91400 Orsay, France · CNRS, MAP5 Université Paris Cité F-75006 Paris, France · Department of Mathematical Sciences and Pioneer Centre for Artificial Intelligence, University of Copenhagen, Denmark

Causal Discovery Causal Identifiability

May 6, 2026

MOSAIC: Module Discovery via Sparse Additive Identifiable Causal Learning for Scientific Time Series

Causal representation learning (CRL) seeks to recover latent variables with identifiability guarantees, typically up to permutation and component-wise reparameterization under appropriate assumptions. However, identifiability does not imply interpretability: latent semantics are typically assigned post hoc by alignment with known ground-truth factors. This limitation is particularly acute in scientific time series, where underlying mechanisms are unknown and discovering interpretable structure is a primary goal. In contrast, scientific observations (such as residue-pair distances, climate indices, or process sensors) are inherently semantic, as they correspond to named physical quantities. This raises a key question: can the interpretability of observations be transferred to the identifiable latent space? We propose MOSAIC (Module discovery via Sparse Additive Identifiable Causal learning), a sparse temporal VAE that integrates temporal CRL identifiability with support recovery over observed variables. MOSAIC identifies latent variables via regime-conditioned temporal variation, and recovers for each latent a sparse set of associated observations through an additive decoder, yielding module-level interpretability. We show that ANOVA main-effect supports are identifiable under general smooth mixing functions, with finite-sample recovery guarantees for a group-lasso estimator and empirical evaluation of MOSAIC's entropy regularizer. Empirically, MOSAIC recovers domain-consistent variable groups across RNA molecular dynamics, solar wind, ENSO climate, the Tennessee Eastman process, and a synthetic tokamak benchmark, enabling interpretable discovery of latent mechanisms in scientific time series.

Shicheng Fan, Nour Elhendawy, Jianle Sun +4

University of Illinois Chicago · Case Western Reserve University · Carnegie Mellon University +1

Causal Representation Learning Causal Identifiability

May 6, 2026

Causal discovery under mean independence and linearity

Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.

Geert Mesters, Alvaro Ribot, Anna Seigal +1

Structural Causal Models Causal Discovery Causal Identifiability

May 5, 2026

Partially Observed Structural Causal Models

Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.

Turan Orujlu, Jordan Matelsky, Martin V. Butz +2

University of Tübingen · MPI for Biological Cybernetics · University of Pennsylvania +1

Structural Causal Models Causal Identifiability Causal Intervention

Apr 28, 2026

Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time

Causal inference in continuous-time sequential decision problems is challenged by hidden confounding and partially observed states. We show that, under explicit structural assumptions, observability of the latent state enables identification of dynamic treatment effects through a continuous-time conditional front-door adjustment, even in the presence of hidden confounding. We derive a general adjustment formula and show that it reduces to a tractable state-space formula when unobserved contemporaneous disturbances are temporally uncorrelated. This formula expresses potential-outcome distributions under alternative treatment trajectories through the measurement model, latent dynamics, and the filtering distribution over latent states. We propose Observable Neural ODEs (ObsNODEs), Neural ODE models in observable normal form that implement this tractable adjustment for causal forecasting. ObsNODEs learn continuous-time dynamics with states reconstructible from observations, enabling outcome prediction under alternative treatment paths. Experiments on synthetic, semi-synthetic, and real-world clinical data demonstrate strong performance over recent sequence models, including external validation.

Jennifer Wendland, Nicolas Freitag, Maik Kschischo

Department of Computer Science University of Koblenz 53424 Koblenz, Germany

Causal Effect Estimation Clinical Outcome Prediction Causal Identifiability Causal Inference Neural ODEs

Apr 26, 2026

Causal Representation Learning from General Environments under Nonparametric Mixing

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

Ignavier Ng, Shaoan Xie, Xinshuai Dong +2

1Carnegie Mellon University · 2Mohamed bin Zayed University of Artificial Intelligence

Causal Representation Learning Causal Discovery Causal Structure Learning Causal Identifiability

Apr 22, 2026

Efficient Symbolic Computations for Identifying Causal Effects

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

Benjamin Hollering, Pratik Misra, Nils Sturma

Max Planck Institute for Mathematics in the Sciences, Germany · Binghamton University, USA · École Polytechnique Fédérale de Lausanne, Switzerland

Structural Causal Models Symbolic Reasoning Causal Identifiability

Apr 14, 2026

Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing

Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.

Danru Xu, Sébastien Lachapelle, Sara Magliacane

University of Amsterdam · Samsung AI Lab, Montreal · Saarland University & University of Amsterdam

Causal Representation Learning Representation Identifiability Causal Identifiability Gaussian Mixture Models

Apr 10, 2026

Iterative Identification Closure: Amplifying Causal Identifiability in Linear SEMs

The Half-Trek Criterion (HTC) is the primary graphical tool for determining generic identifiability of causal effect coefficients in linear structural equation models (SEMs) with latent confounders. However, HTC is inherently node-wise: it simultaneously resolves all incoming edges of a node, leaving a gap of "inconclusive" causal effects (15-23% in moderate graphs). We introduce Iterative Identification Closure (IIC), a general framework that decouples causal identification into two phases: (1) a seed function S_0 that identifies an initial set of edges from any external source of information (instrumental variables, interventions, non-Gaussianity, prior knowledge, etc.); and (2) Reduced HTC propagation that iteratively substitutes known coefficients to reduce system dimension, enabling identification of edges that standard HTC cannot resolve. The core novelty is iterative identification propagation: newly identified edges feed back to unlock further identification -- a mechanism absent from all existing graphical criteria, which treat each edge (or node) in isolation. This propagation is non-trivial: coefficient substitution alters the covariance structure, and soundness requires proving that the modified Jacobian retains generic full rank -- a new theoretical result (Reduced HTC Theorem). We prove that IIC is sound, monotone, converges in O(|E|) iterations (empirically <=2), and strictly subsumes both HTC and ancestor decomposition. Exhaustive verification on all graphs with n<=5 (134,144 edges) confirms 100% precision (zero false positives); with combined seeds, IIC reduces the HTC gap by over 80%. The propagation gain is gamma~4x (2 seeds identifying ~3% of edges to 97.5% total identification), far exceeding gamma<=1.2x of prior methods that incorporate side information without iterative feedback.

Ziyi Ding, Xiao-Ping Zhang

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China

Causal Identifiability Structural Causal Models

Apr 10, 2026

Identifying Causal Effects Using a Single Proxy Variable

Unobserved confounding is a key challenge when estimating causal effects from a treatment on an outcome. In this work, we assume that we observe a single, potentially multi-dimensional proxy variable of the unobserved confounder and that we know the mechanism that generates the proxy from the confounder. Under an assumption called Single Proxy Identifiability of Causal Effects or simply SPICE, we prove that this error mechanism is complete and causal effects are identifiable. We extend the proxy-based causal identifiability results by Kuroki and Pearl (2014); Pearl (2010) to multi-dimensional continuous settings, more flexible functional relationships and a broader class of distributions. Further, we develop a neural network based estimation framework, SPICE-Net, to estimate causal effects, which is applicable to both discrete and continuous treatments.

Silvan Vollmer, Niklas Pfister, Sebastian Weichwald

Department of Mathematical Sciences University of Copenhagen Copenhagen, Denmark · Lakera AI Zurich, Switzerland

Causal Effect Estimation Causal Inference with Unobserved Confounding Causal Inference Causal Identifiability

Apr 1, 2026

The Digital Twin Counterfactual Framework: A Validation Architecture for Simulated Potential Outcomes

The fundamental problem of causal inference - that the counterfactual outcome for any individual is never observed - has shaped the entire methodology of the field. Every existing approach substitutes assumptions for missing data: ignorability, parallel trends, exclusion restrictions. None produces the counterfactual itself. This paper proposes the Digital Twin Counterfactual Framework (DTCF): rather than estimating the counterfactual statistically, we simulate it using a digital twin and subject the simulation to a hierarchical validation regime. We formalize the digital twin simulator as a stochastic mapping within the potential outcomes framework and introduce a hierarchy of twin fidelity assumptions - from marginal fidelity through joint fidelity to structural fidelity - each unlocking a progressively richer class of estimands. The central contribution is threefold. First, a five-level validation architecture converts the unfalsifiable claim that the simulator produces correct counterfactuals into falsifiable tests against observable data. Second, a formal decomposition separates causal quantities into those that are marginally validated (ATE, CATE, QTE - testable through observable-arm comparison) and those that are copula-dependent (the ITE distribution, probability of benefit/harm, variance of treatment effects - permanently reliant on the unobservable within-individual dependence structure). Third, bounding, sensitivity, and uncertainty quantification tools make the copula dependence explicit. The DTCF does not resolve the fundamental problem of causal inference. What it provides is a framework in which marginal causal claims become increasingly testable, joint causal claims become explicitly assumption-indexed, and the gap between the two is formally characterized.

Olav Laudy

Counterfactual Evaluation Causal Effect Estimation Causal Reasoning Causal Identifiability Digital Twins

Mar 23, 2026

Causal Discovery in Action: Learning Chain-Reaction Mechanisms from Interventions

Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit directional, cascade-like structure, in which components activate sequentially and upstream failures suppress downstream effects. We study causal discovery in such chain-reaction systems and show that the causal structure is uniquely identifiable from blocking interventions that prevent individual components from activating. We propose a minimal estimator with finite-sample guarantees, achieving exponential error decay and logarithmic sample complexity. Experiments on synthetic models and diverse chain-reaction environments demonstrate reliable recovery from a few interventions, while observational heuristics fail in regimes with delayed or overlapping causal effects.

Panayiotis Panayiotou, Özgür Şimşek

Department of Computer Science, University of Bath, UK

Causal Discovery Causal Identifiability Causal Intervention

Mar 15, 2026

Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability

Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.

Amir Saki, Usef Faghihi

Université du Québec à Trois-Rivières (UQTR).

Causal Effect Estimation Causal Identifiability Conditional Average Treatment Effect Estimation Persistent Homology

Mar 10, 2026

Proxy-Guided Measurement Calibration

Aggregate outcome variables collected through surveys and administrative records are often subject to systematic measurement error. For instance, in disaster loss databases, county-level losses reported may differ from the true damages due to variations in on-the-ground data collection capacity, reporting practices, and event characteristics. Such miscalibration complicates downstream analysis and decision-making. We study the problem of outcome miscalibration and propose a framework guided by proxy variables for estimating and correcting the systematic errors. We model the data-generating process using a causal graph that separates latent content variables driving the true outcome from the latent bias variables that induce systematic errors. The key insight is that proxy variables that depend on the true outcome but are independent of the bias mechanism provide identifying information for quantifying the bias. Leveraging this structure, we introduce a two-stage approach that utilizes variational autoencoders to disentangle content and bias latents, enabling us to estimate the effect of bias on the outcome of interest. We analyze the assumptions underlying our approach and evaluate it on synthetic data, semi-synthetic datasets derived from randomized trials, and a real-world case study of disaster loss reporting.

Saketh Vishnubhatla, Shu Wan, Andre Harrison +2

Arizona State University, Tempe, AZ · DEVCOM Army Research Lab, Adelphi, MD

Proximal Causal Inference Causal Inference Causal Identifiability

Mar 9, 2026

Structural Causal Bottleneck Models

We introduce structural causal bottleneck models (SCBMs), a novel class of structural causal models in which causal effects between high-dimensional variables are mediated by low-dimensional summary statistics, or bottlenecks. SCBMs provide a flexible framework for mechanism-specific, target-dependent dimension reduction while remaining estimable via standard learning algorithms. We prove that bottleneck variables are identifiable up to bijection from observational data, and validate this experimentally. We then study causal effect estimation in linear SCBMs under three standard adjustment strategies. For instrumental variables, we identify a population-level non-identifiability of naïve two-stage least squares when all variables are high-dimensional, and show that bottleneck representations restore identification. For mediation and backdoor adjustment, we prove that conditioning on bottleneck variables yields valid effect estimates with explicit finite-sample efficiency gains over conditioning on full high-dimensional variables. We argue that SCBMs provide a principled alternative to existing causal dimension reduction frameworks such as causal representation learning and causal abstractions.

Simon Bing, Jonas Wahl, Jakob Runge

Equal contribution · Technische Universität Berlin · Department of Computer Science, University of Potsdam +1

Structural Causal Models Causal Effect Estimation Causal Identifiability

Mar 9, 2026

Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems

We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Therefore, rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrisations compatible with that structure. This leads to a trichotomy of edge-sign identifiability: identifiable, non-identifiable, and partially identifiable. This trichotomy introduces the new notion of partial identifiability to the literature, which we show is a genuine category in our setting. Under a notion of faithfulness, we derive criteria to identify membership of each category for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix.

Gijs van Seeventer, Saber Salehkaleybar

1LIACS, Leiden University, Netherlands

Stochastic Differential Equations Structural Causal Models Causal Identifiability

Mar 5, 2026

Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning

Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.

Haoyue Dai, Immanuel Albrecht, Peter Spirtes +1

Carnegie Mellon University · FernUniversität in Hagen · MBZUAI

Causal Discovery Causal Discovery with Latent Confounding Causal Identifiability Structural Causal Models

Mar 3, 2026

Scalable Contrastive Causal Discovery under Unknown Soft Interventions

Observational causal discovery is only identifiable up to the Markov equivalence class. While interventions can reduce this ambiguity, in practice interventions are often soft with multiple unknown targets. In many realistic scenarios, only a single intervention regime is observed. We propose a scalable causal discovery model for paired observational and interventional settings with shared underlying causal structure and unknown soft interventions. The model aggregates subset-level PDAGs and applies contrastive cross-regime orientation rules to construct a globally consistent maximal PDAG under Meek closure, enabling generalization to both in-distribution and out-of-distribution settings. Theoretically, we prove that our model is sound with respect to a restricted

Ψ

equivalence class induced solely by the information available in the subset-restricted setting. We further show that the model asymptotically recovers the corresponding identifiable PDAG and can orient additional edges compared to non-contrastive subset-restricted methods. Experiments on synthetic data demonstrate improved causal structure recovery, generalization to unseen graphs with held-out causal mechanisms, and scalability to larger graphs, with ablations supporting the theoretical results.

Mingxuan Zhang, Khushi Desai, Sopho Kevlishvili +1

Department of Systems Biology, Columbia University · Irving Institute for Cancer Dynamics, Columbia University · Department of Computer Science, Columbia University +2

Causal Discovery Structural Causal Models Causal Identifiability Causal Intervention

Mar 1, 2026

SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry

Reliable decision-making in complex multi-agent systems requires calibrated predictions and interpretable uncertainty. We introduce SphUnc, a unified framework combining hyperspherical representation learning with structural causal modeling. The model maps features to unit hypersphere latents using von Mises-Fisher distributions, decomposing uncertainty into epistemic and aleatoric components through information-geometric fusion. A structural causal model on spherical latents enables directed influence identification and interventional reasoning via sample-based simulation. Empirical evaluations on social and affective benchmarks demonstrate improved accuracy, better calibration, and interpretable causal signals, establishing a geometric-causal foundation for uncertainty-aware reasoning in multi-agent settings with higher-order interactions.

Rong Fu, Chunlei Meng, Jinshuo Liu +8

Independent Researcher

Uncertainty Decomposition Uncertainty Calibration Multi-Agent Reasoning Causal Identifiability Structural Causal Models Hyperspherical Representation Learning

Mar 1, 2026

Robust Weighted Triangulation of Causal Effects Under Model Uncertainty

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and possibly partially overlapping, sets of identifying assumptions to infer the causal effect, a process known as triangulation. Principled methods for triangulation, however, remain underdeveloped. Here, we develop a framework for causal effect triangulation that combines model testability methods from causal discovery with statistical inference methods from semiparametric theory, while avoiding explicit model selection and post-selection inference problems. We propose a triangulation functional that combines identified functionals from each model with data-driven measures of model validity. We provide a bound on the distance of the functional from the true causal effect along with conditions under which this distance can be taken to zero. Finally, we derive valid statistical inference for this functional. Our framework formalizes robustness under causal pluralism without requiring agreement across models or commitment to a single specification. We demonstrate its performance through simulations and an empirical application.

Rohit Bhattacharya, Ina Ocelli, Ted Westling

Dept. of Computer Science, Williams College · Dept. of Mathematics and Statistics, University of Massachusetts Amherst

Semiparametric Inference Causal Effect Estimation Causal Identifiability

Feb 27, 2026

Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data

Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However, standard causal discovery does not reveal which causes act on the mean versus the variance, as it returns a single moment-agnostic graph, limiting interpretability and downstream intervention design. We propose a Bayesian, moment-driven causal discovery framework that infers separate mean and variance causal graphs from observational heteroscedastic data. We first derive the identification results by establishing sufficient conditions under which these two graphs are separately identifiable. Building on this theory, we develop a variational inference method that learns a posterior distribution over both graphs, enabling principled uncertainty quantification of structural features (e.g., edges, paths, and subgraphs). To address the challenges of parameter optimization in heteroscedastic models with two graph structures, we take a curvature-aware optimization approach and develop a prior incorporation technique that leverages domain knowledge on node orderings, improving sample efficiency. Experiments on synthetic, semi-synthetic, and real data show that our approach accurately recovers mean and variance structures and outperforms state-of-the-art baselines.

Yoichi Chikahara

Communication Science Laboratories, NTT, Inc., Kyoto, Japan

Causal Discovery Causal Identifiability

Feb 26, 2026

Causal Identification from Counterfactual Data: Completeness and Bounding Results

Previous work establishing completeness results for counterfactual identification has been circumscribed to the setting where the input data belongs to observational or interventional distributions (Layers 1 and 2 of Pearl's Causal Hierarchy), since it was generally presumed impossible to obtain data from counterfactual distributions, which belong 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 realizability. This leaves open the question of what additional counterfactual quantities now become identifiable, given this new access to (some) Layer 3 data. To answer this question, we develop the CTFIDU+ algorithm for identifying counterfactual queries from an arbitrary set of Layer 3 distributions, and prove that it is complete for this task. Building on this, we establish the theoretical limit of which counterfactuals can be identified from physically realizable distributions, thus implying the fundamental limit to exact causal inference in the non-parametric setting. Finally, given the impossibility of identifying certain critical types of counterfactuals, we derive novel analytic bounds for such quantities using realizable counterfactual data, and corroborate using simulations that counterfactual data helps tighten the bounds for non-identifiable quantities in practice.

Arvind Raghavan, Elias Bareinboim

Causal Artificial Intelligence Lab, Department of Computer Science, Columbia University

Causal Inference Causal Identifiability Partial Identification

Feb 24, 2026

CausalReasoningBenchmark: A Real-World Benchmark for Disentangled Evaluation of Causal Identification and Estimation

Many benchmarks for automated causal inference evaluate a system's performance based on a single numerical output, such as an Average Treatment Effect (ATE). This approach conflates two distinct steps in causal analysis: identification, formulating a valid research design under stated assumptions, and estimation, implementing that design numerically on finite data. We introduce CausalReasoningBenchmark, a benchmark of 174 queries across 139 real-world datasets, curated from 73 peer-reviewed research papers and three widely used causal-inference textbooks. For each query, a system must produce (i) a structured identification specification that names the strategy, the treatment, outcome, and control variables, and all design-specific elements, and (ii) a point estimate with a standard error. By scoring these two components separately, our benchmark enables granular diagnosis: it distinguishes failures in causal reasoning from errors in numerical execution. Baseline results with a state-of-the-art LLM show that, while the model correctly identifies the high-level strategy in 81% of cases, full identification-specification correctness drops to only 38%, revealing that the bottleneck lies in the nuanced details of research design rather than in computation. CausalReasoningBenchmark is publicly available on Hugging Face and is designed to foster the development of more robust automated causal-inference systems.

Ayush Sawarni, Jiyuan Tan, Vasilis Syrgkanis

Stanford University

Causal Effect Estimation Benchmark Design Causal Identifiability Causal Reasoning Causal Inference

Feb 23, 2026

Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning

Mendelian Randomization (MR) is a prominent observational epidemiological research method designed to address unobserved confounding when estimating causal effects. However, core assumptions -- particularly the independence between instruments and unobserved confounders -- are often violated due to population stratification or assortative mating. Leveraging the increasing availability of multi-environment data, we propose a representation learning framework that exploits cross-environment invariance to recover latent exogenous components of genetic instruments. We provide theoretical guarantees for identifying these latent instruments under various mixing mechanisms and demonstrate the effectiveness of our approach through simulations and semi-synthetic experiments using data from the All of Us Research Hub.

Shimeng Huang, Matthew Robinson, Francesco Locatello

Institute of Science and Technology Austria (ISTA)

Instrumental Variable Estimation Causal Identifiability Invariant Representation Learning

Feb 21, 2026

Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete ordinal outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.

Naoya Hashimoto, Yuta Kawakami, Jin Tian

Mohamed bin Zayed University of Artificial Intelligence

Monotonicity Constraints Causal Identifiability Partial Identification

Feb 16, 2026

Bounding Probabilities of Causation with Partial Causal Diagrams

Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates, require complete causal graphs, or rely on restrictive binary settings, limiting their practical use. In real-world applications, causal information is often partial but nontrivial. This paper proposes a general framework for bounding probabilities of causation using partial causal information. We show how the available structural or statistical information can be systematically incorporated as constraints in a optimization programming formulation, yielding tighter and formally valid bounds without full identifiability. This approach extends the applicability of probabilities of causation to realistic settings where causal knowledge is incomplete but informative.

Yuxuan Xie, Ang Li

University of Ottawa, Ontario, Canada · Department of Computer Science, Florida State University, FL, U.S.A.

Causal Inference Causal Identifiability

Jan 30, 2026

Uncertainty-aware Causal Decision Making via Effect Bound Decomposition

Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

Md Musfiqur Rahman, Ziwei Jiang, Hilaf Hasson +1

Electrical and Computer Engineering, Purdue University · Computer Science, Johns Hopkins University · Cohesity

Causal Effect Estimation Parameter Identifiability Partial Identification Causal Identifiability Decision-Making under Uncertainty Causal Inference with Unobserved Confounding

Jan 29, 2026

TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Shicheng Fan, Kun Zhang, Lu Cheng

University of Illinois at Chicago · Carnegie Mellon University · Mohamed bin Zayed University of Artificial Intelligence

Causal Representation Learning Causal Identifiability