Causal Identifiability

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11 papers in the last four weeks, up 83% on the four weeks before. 0.1% of all new papers.

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May 13, 2026stat.ME

Towards a holistic understanding of Selection Bias for Causal Effect Identification

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. 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.

Yiwen Qiu, Filip Kovačević, Shimeng Huang +2

Institute of Science and Technology Austria (ISTA) · Carnegie Mellon University

Causal Effect Estimation Data Selection Causal Identifiability Selection Bias

May 13, 2026cs.LG

IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning

The instrumental-variables (IV) setting is standard for partial identification of causal effects when unobserved confounding makes point identification impossible. Existing approaches face methodological bottlenecks: closed-form bound estimands are required -- e.g., Balke-Pearl equations in binary IV -- and even when available, designing accurate estimators requires manual effort tailored to each estimand. While direct Bayesian inference of the causal effects, instead of the bounds, circumvents these challenges, it is often computationally intensive and suffers from high prior sensitivity or under-dispersed posteriors. As a remedy, we introduce IV-ICL, an amortized Bayesian in-context learning method that learns the marginal posterior distribution of the causal effects directly and derives bounds as its quantiles. Unlike standard variational inference that optimizes exclusive KL divergence, amortized Bayesian inference minimizes the expected inclusive KL, a mass-covering objective. We empirically observe that optimizing inclusive KL can recover the entire identified set across diverse data-generating processes, while exclusive-KL (e.g. with variational inference) of the same Bayesian formulation collapses onto a single mode and fails to cover the identified set. We evaluate IV-ICL on synthetic and semi-synthetic IV benchmarks and show it produces intervals that are more reliably valid and more informative compared to efficient semi-parametric, Bayesian, and plug-in baselines, at 20-500x lower inference time. Beyond methodology, we propose a procedure to convert randomized controlled trials into IV benchmarks with provably preserved ground-truth causal effects that enables a more realistic evaluation of partial-identification methods.

Vahid Balazadeh, Hamidreza Kamkari, Medha Barath +2

University of Toronto · Vector Institute · MIT CSAIL +1

Causal Effect Estimation Parameter Identifiability Amortized Inference Partial Identification Causal Identifiability In-Context Learning+2

May 11, 2026stat.ML

Coarsening Linear Non-Gaussian Causal Models with Cycles

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.

Francisco Madaleno, Francisco C Pereira, Alex Markham

Department of Technology, Management and Economics, Technical University of Denmark · Department of Mathematical Sciences,11 University of Copenhagen

Structural Causal Models Causal Discovery Causal Structure Learning Causal Abstraction Causal Identifiability

May 11, 2026cs.LG

Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions

We propose SVAR-FM (Structural VAR with Flow Matching), a framework for time series causal discovery that treats a physics-based simulator as a mechanical realization of Pearl's do operator. Clamping a variable inside the simulator physically severs confounding paths, producing interventional data by construction. Conditional Flow Matching then learns the nonlinear interventional conditionals. Theoretically, we prove that the full structural VAR becomes identifiable under a coverage condition on the simulator-clampable variables, and derive an end-to-end error bound that decomposes into Monte Carlo, simulator fidelity, and Flow Matching terms. A sign-flip corollary predicts that when simulator accuracy falls below a threshold, the estimated causal effect reverses sign. Empirically, a benchmark across four scientific domains confirms that SVAR-FM recovers the correct causal sign where observational methods produce sign-reversed estimates due to confounding. A case study in ultrafast laser physics verifies the sign-flip prediction by physically varying the accuracy level of a first-principles quantum solver: the low-accuracy setting reverses the causal sign, while the high-accuracy setting recovers the correct direction (R-squared = 0.983, zero bias).

Tsuyoshi Okita

Kyushu Institute of Technology

Time-Series Causal Discovery Causal Discovery Causal Identifiability

May 9, 2026cs.AI

CIVeX: Causal Intervention Verification for Language Agents

A valid tool call is not necessarily a valid intervention. Tool-using language agents are guarded by schema validators, policy filters, provenance checks, state predictors, and self-verification, yet such safeguards do not certify that a state-changing action has an identifiable causal effect. In confounded workflows, the action that looks optimal in observational logs can reduce utility when executed. We introduce CIVeX, a causal intervention verifier that maps proposed actions to structural causal queries over a committed action-state graph, checks identifiability, and returns one of four auditable verdicts: EXECUTE, REJECT, EXPERIMENT, or ABSTAIN. Execution requires an assumption-scoped causal certificate carrying graph commitments, an identification argument, a one-sided lower confidence bound (LCB), provenance, and risk limits. On Causal-ToolBench (1,890 instances, 7 seeds), CIVeX yields zero observed false executions across moderate and adversarial confounding. Under adversarial confounding it reaches 84.9% accuracy and 81.1% of oracle utility (+2.23 vs +2.76) and is the only non-oracle method whose constrained utility under a zero-false-execution constraint exceeds the AlwaysAbstain floor. On IHDP and ZOZO Open Bandit (real production logs with uniform-random ground truth), CIVeX matches Oracle correct-execution within 0.1pp and cuts per-execute false-execution by >=50x over naive baselines. A chain-of-thought LLM verifier (Claude Opus, Sonnet) cuts false-execution by an order of magnitude over a terse baseline, yet under adversarial confounding Opus's utility falls to 74% of CIVeX's. Intervention identifiability, not action validity, is the missing primitive for reliable tool use.

Fabio Rovai

The Tesseract Academy

Structural Causal Models Tool-Using Agents Causal Identifiability LLM Agent Reliability

May 8, 2026cs.LG

Position: Mechanistic Interpretability Must Disclose Identification Assumptions for Causal Claims

Mechanistic interpretability papers increasingly use causal vocabulary: circuits, mediators, causal abstraction, monosemanticity. Such claims require explicit identification assumptions. A purposive audit of 10 papers across four methodological strands finds no dedicated identification-assumptions section and a recurring pattern: validation metrics such as faithfulness, completeness, monosemanticity, alignment, or ablation effects are reported as causal support without stating the assumptions that make them identifying. A two-human-coder audit on

n=30

reproduces the direction of the main finding: dedicated identification sections are absent, and validation-metric substitution is common, though exact Dim B/D counts are coding-rule sensitive. The paper proposes a disclosure norm: state whether the claim is causal, name the identification strategy, enumerate assumptions, stress at least one, and explain how conclusions shift if assumptions fail. Validation is not identification.

Zezheng Lin, Fengming Liu

Preprint.

Mechanistic Interpretability Causal Identifiability Causal Interpretability Explainability Evaluation

May 8, 2026stat.ML

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, 2026cs.AI

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 · UC Berkeley

Causal Effect Estimation Partial Identification Causal Identifiability Causal Inference Causal Intervention

May 7, 2026stat.ME

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, 2026cs.LG

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, and provide finite-sample recovery guarantees for a tractable sparse-additive variant. 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, 2026stat.ME

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, 2026cs.LG

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, 2026cs.LG

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, 2026cs.LG

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, 2026stat.ML

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

Mar 9, 2026math.ST

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 1, 2026stat.ME

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 24, 2026cs.AI

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

Jan 30, 2026cs.LG

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

Jan 29, 2026cs.LG

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

May 21, 2025stat.ML

Clustering and Pruning in Causal Data Fusion

Data fusion, the process of combining observational and experimental data, can enable the identification of causal effects that would otherwise remain non-identifiable. Although identification algorithms have been developed for specific scenarios, do-calculus remains the only general-purpose tool for causal data fusion, particularly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increases and the causal graph grows in complexity. Consequently, there exists a need to reduce the size of such models while preserving the essential features. For this purpose, we propose pruning (removing unnecessary variables) and clustering (combining variables) as preprocessing operations for causal data fusion. We generalize earlier results on a single data source and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identifiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corresponding identifying functional for identifiable causal effects. Examples from epidemiology and social science demonstrate the use of the results.

Otto Tabell, Santtu Tikka, Juha Karvanen

Department of Mathematics and Statistics FI-40014 University of Jyvaskyla, Finland

Clustering Causal Identifiability

Feb 27, 2025cs.LG

Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms

Causal discovery is a difficult problem that typically relies on strong assumptions on the data-generating model, such as non-Gaussianity. In practice, many modern applications provide multiple related views of the same system, which has rarely been considered for causal discovery. Here, we leverage this multi-view structure to achieve causal discovery with weak assumptions. We propose a multi-view linear Structural Equation Model (SEM) that extends the well-known framework of non-Gaussian disturbances by alternatively leveraging correlation over views. We prove the identifiability of the model for acyclic SEMs. Subsequently, we propose several multi-view causal discovery algorithms, inspired by single-view algorithms (DirectLiNGAM, PairwiseLiNGAM, and ICA-LiNGAM). The new methods are validated through simulations and applications on neuroimaging data, where they enable the estimation of causal graphs between brain regions.

Ambroise Heurtebise, Omar Chehab, Pierre Ablin +2

Inria, CEA, University of Paris-Saclay, France · University of Carnegie Mellon, Pittsburgh PA, USA · Apple +1

Structural Causal Models Causal Discovery Causal Identifiability

Feb 27, 2025cs.LG

Causal Effect Estimation under Networked Interference without Networked Unconfoundedness Assumption

Estimating causal effects under networked interference from observational data is a crucial yet challenging problem. Most existing methods mainly rely on the networked unconfoundedness assumption, which guarantees the identification of networked effects. However, this assumption is often violated due to the latent confounders inherent in observational data, thereby hindering the identification of networked effects. To address this issue, we leverage the rich interaction patterns between units in networks, which provide valuable information for recovering these latent confounders. Building on this insight, we develop a confounder recovery framework that explicitly characterizes three categories of latent confounders in networked settings: those affecting only the unit, those affecting only the unit's neighbors, and those influencing both. Based on this framework, we design a networked effect estimator using identifiable representation learning techniques. From a theoretical standpoint, we prove the identifiability of all three types of latent confounders and, by leveraging the recovered confounders, establish a formal identification result for networked effects. Extensive experiments validate our theoretical findings and demonstrate the effectiveness of the proposed method.

Weilin Chen, Ruichu Cai, Jie Qiao +2

School of Computer Science, Guangdong University of Technology, Guangzhou, 510006, China · School of Computer Science, Guangdong University of Technology, Guangzhou, 510006, China and Peng Cheng Laboratory, Shenzhen, China · Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom

Causal Effect Estimation Causal Identifiability Causal Inference

Oct 29, 2024stat.ML

Identifiability Analysis of Linear ODE Systems with Hidden Confounders

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time

t

. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Yuanyuan Wang, Biwei Huang, Wei Huang +2

The University of Melbourne · University of California, San Diego

Parameter Identifiability Causal Identifiability Causal Inference

Jul 10, 2024stat.ML

Towards Complete Causal Explanation with Expert Knowledge

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.

Aparajithan Venkateswaran, Emilija Perković

Microsoft · Redmond, WA 98052, USA · Department of Statistics +2

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

Nov 13, 2023cs.LG

Causal Discovery in Mixtures of Populations

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.

Bijan Mazaheri, Spencer Gordon, Yuval Rabani +1

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA · Fragment Data Technologies, San Francisco, California, USA · Department of Computer Science, Hebrew Univeristy of Jerusalem, Jerusalem, Israel +1

Latent Variable Models Causal Discovery Causal Identifiability Causal Discovery with Latent Confounding