Time-Series Causal Discovery

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6 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

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Latest papers 36

Oct 4, 2026cs.LG

Delay-coordinate reconstruction and conditional-moment causal diagnostics in stochastic systems

Partial observation and delay-coordinate reconstruction are rooted in deterministic dynamical-systems theory, whereas there are many systems with intrinsic stochasticity. We propose a conditional-moment interpretation of delay-coordinate reconstruction for stochastic systems, in which a delay vector is used to reconstruct conditional moments of a future distribution rather than a unique future sample path. Two complementary arguments motivate this viewpoint. First, the probability density of a stochastic differential equation obeys a deterministic Fokker-Planck equation and, under certain assumptions, is represented by an infinite deterministic hierarchy of moments. Hence, a finite-moment closure suggests a Takens-like finite-dimensional approximation. Second, a discussion based on the Koopman operator theory clarifies that the time evolution of an observable in the Mori-Zwanzig formalism yields a conditional expectation in stochastic systems. Then, the orthogonal "noise" term in the coefficient-space Mori-Zwanzig equation vanishes in the stochastic cases; this result is consistent with the moment-based argument. As an application of this stochastic delay-reconstruction viewpoint, we revisit convergent cross mapping (CCM) for diagnosing certain causal relationships. Although CCM based on the embedding theorem cannot generally be applied to stochastic systems, it is possible to examine certain types of causal relationships by using conditional moments. Using coupled logistic systems with additive and multiplicative coupling mechanisms, we discuss how causal relationships are embedded in stochastic systems.

Jun Ohkubo

Graduate School of Science and Engineering, Saitama University, Sakura, Saitama, 338–8570 Japan

Dynamical Systems Stochastic Linear Dynamical Systems Time-Series Causal Discovery Conditional Distribution Estimation

Oct 4, 2026stat.ME

Causal Lag Structure Discovery in Confounded Time Series via Orthogonalized Adaptive Estimation

Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal lag estimation (ACLE) picks the lag order at each time step by sequential significance tests, tracking regime changes. Third, entry-wise

z

-tests with Benjamini--Hochberg correction select directed edges at a target FDR. We prove that in each rolling window, the debiased coefficients are asymptotically normal around a window-averaged target, so their

z

-tests are asymptotically valid. On a synthetic benchmark with time-varying structure and nonlinear confounding, ORACLE-VARX (LightGBM) tracks the true lag order best (RMSE

0.96

vs

1.1

--

1.5

), has edge FDR

0.047

, close to PCMCI (

0.045

) and below VAR (

0.129

) and VAR-LiNGAM (

0.187

), and forecasts better than all three. On nine U.S. sector ETFs with macroeconomic confounders, it yields interpretable causal graphs whose lag order rises in high-volatility regimes.

Hong Kiat Tan, Isaac-Neil Zanoria, James Chen +2

Department of Mathematics, University of California, Los Angeles · Department of Electrical and Computer Engineering, University of California, Los Angeles · Oxford-Man Institute of Quantitative Finance, University of Oxford +1

Debiased ML Time-Series Causal Discovery

Sep 30, 2026cs.AI

Inferring Causal Relations between Two Sequences of Events with Language Models

Causal AI is a branch of Artificial Intelligence which helps understand and reason about cause and effect relationships, not just patterns or correlations. Causal discovery aims to infer elements of the underlying causal structure--often represented as a directed graph--from observational and, when available, interventional data. While causal discovery is the fundamental step for moving beyond mere associations toward genuine understanding, and thus the basic building block of causal AI, it becomes intrinsically difficult when causal relations must be inferred from single observations. In such situations, standard causal discovery methods cannot be used and one has to identify causal relations from limited amount of information. This is typically the case for, e.g., sequences of events produced by different alarms which need to be analyzed on the fly to detect abnormal phenomena, which are usually rare. We show in this study that it is possible to leverage the predictive power of Large Language Models (LLMs) to infer causal relations between only two sequences of events. This approach, which is validated on both synthetic and real data, provides better results than standard causal discovery algorithms on several time series data, even though these data were converted into smaller, single observed sequences.

Nishchal Prasad, Eric Gaussier, Emilie Devijver +3

INRIA, Univ. Grenoble Alpes, CNRS, LIG · Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG · Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG +1

Time-Series Causal Discovery Causal Discovery Causal Reasoning in Language Models

Sep 28, 2026stat.ME

Forecast-Necessary Causal Discovery for Nonlinear Political Panel Data: Feedback, Functional Form, and the Dynamics of Democratization

A non-significant coefficient in a dynamic panel model need not imply the absence of a relationship. It may instead reflect heterogeneous effects averaged toward zero, reciprocal dynamics overlooked by a recursive specification, or relationships masked by the omission of correlated covariates. Standard linear estimators cannot distinguish among these possibilities. We develop an inferential workflow for political panel data that resolves this ambiguity by combining flexible autoregressive estimation, forecast-necessity testing, functional characterization, and same-data linear benchmarking. The workflow first identifies relationships required for out-of-sample prediction, then characterizes their functional form across political contexts, and finally, distinguishes differences arising from estimator flexibility from those due to model specification. Applied to the causal sequence model of democratization on the V-Dem panel of 113 countries, the workflow reproduces the model's central finding - the protective belt of civil society, the rule of law, and institutionalized parties - while recovering reciprocal relationships from democracy to its institutional supports that a linear model cannot detect. Most importantly, three weak published direct effects, of which two are null, and one is marginally significant, receive three different diagnoses: one dissolves under the full specification, one reflects heterogeneous effects averaged toward zero, and one was masked by the reduced variable set. The workflow corrects the published record in both directions, removing one relationship and recovering two. More broadly, the workflow provides a framework for evaluating dynamic political theories under a model class capable of representing nonlinear and reciprocal mechanisms while preserving relationship-level interpretation and explicit inferential standards.

Michael Coppedge, Dmitry Zaytsev, Valentina Kuskova

Department of Political Science, University of Notre Dame, Notre Dame, IN, USA · Kellogg Institute, University of Notre Dame, Notre Dame, IN, USA · Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, IN, USA

Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Sep 20, 2026cs.LG

ITSY: Causal Discovery From Irregular Time-Series Data

Structural causal models for time series recover contemporaneous and lagged effects, but most methods require complete observation windows and become misspecified when samples are missing. We introduce ITSY, the first continuous-optimization method for causal discovery from irregular time series under a linear model. ITSY reformulates the structural equation so that prediction uses the nearest available history rather than the possibly missing current slice, and jointly imputes missing values while learning both graphs. A weighted reconstruction objective corrects the noise transformation induced by this reformulation. Across synthetic regimes varying missingness, scale, graph density, and noise, and on a real world benchmark, ITSY consistently improves graph recovery over representative SCM-based baselines, demonstrating the effectiveness of the proposed method. The results establish a focused solution for irregular linear first-order dynamics and clarify the assumptions required for nonlinear or higher-order extensions.

Wenbo Xu, Yue He, Yunhai Wang +2

Renmin University of China, China · Zhejiang University, China

Irregular Time-Series Modeling Structural Causal Models Time-Series Causal Discovery Learning with Missing Data Causal Discovery

Sep 14, 2026cs.LG

Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems

In networked dynamical systems, the parameter of primary mechanistic interest is signed interaction structure. Recovering this structure from perturbation time-series data is a fundamental identification problem, compounded by three coupled obstacles: the combinatorial complexity of interaction architectures, ambiguity of causal attribution under limited interventions, and state-dependent dynamics that confound structural inference. Each obstacle is structural in origin and calls for a structural solution. We address these challenges by adopting a reductionist approach, introducing Fundamental Dynamical Units (FDUs): signed three-node interaction patterns as composable primitives that convert the interaction hypothesis space into a finite, constructive, and tractable representation. We show that local interaction structure determines the perturbation conditions required to disentangle direct from relayed influence, making intervention design a structural consequence of the FDU representation. We embed FDU-regularized structural inference within a physics-informed neural ordinary differential equation (ODE) whose governing-equation constraint transforms structural hypotheses into verifiable dynamical predictions, enabling joint recovery of interaction structure and perturbation-resolved trajectories. Validated on synthetic benchmarks with known ground truth, the framework supports structural commitment, expressed through FDU primitives, motif-prescribed intervention design, and physics-informed learning, as a principled basis for mechanistically interpretable inference in networked dynamical systems.

Nima Nouri

Artificial Intelligence for Science Innovation, AstraZeneca, Waltham, MA, USA

Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Sep 1, 2026cs.LG

Replicating TRACE: A Practitioner's Guide to Its Threshold and Particle Budget

TRACE (Math & Lienhart, arXiv:2602.01135) reads causal graphs over event types out of a pretrained autoregressive sequence model by thresholding a per-position conditional-mutual-information estimate at a fixed tau. We independently replicate its headline synthetic result: with tau selected on a validation split, mean per-sequence F1 against exact interventional truth reaches 0.90-0.91 at vocabulary size 1000 (paper: 0.91) and 0.86-0.91 from 100 to 2000. First, the optimal threshold is pinned to the truth margin, not to any constant: at every size the errors at tau* straddle the delta = 0.05 margin defining ground truth (missed true edges lie just above it, accepted false ones just below), and the blind optimum lands near delta/2 times the estimator's calibration, confirmed out of sample at 5000. Second, at a single global threshold TRACE mostly recovers a direct, adjacent-influence graph: lag-1 true edges are recalled at 0.97-0.99, while true edges at lag 2 or more read orders of magnitude lower---the reading-scale price of randomizing mediating positions, which an exact test of direct causal effect requires when the truth is unknown. A per-lag threshold family recovers a third to a half of lag-2 truth; on lag-uniform data one validated threshold recalls every lag at 0.40-0.87, 8-26 pp below an atomic-intervention control at lags 3-6. Third, the default lag decay of the paper's synthetic benchmark concentrates about 85% of interventional truth at lag 1 and pushes the rest below the estimator's noise floor, so headline F1 there certifies lag-1 recovery only and conflates the benchmark's skew with the algorithm's own limit; a flatter decay separates the two. Fourth, F1 saturates from N = 2 particles at the selected threshold---a property of the threshold's margin over the noise floor, not of the estimator, which converges as N^(-1/2). We distill five practitioner rules.

Alex Chadyuk, Alicia Zhang, Roy Kucukates

LotusFlare Inc.

Time-Series Causal Discovery Causal Discovery

Jul 31, 2026cs.LG

AutoCause: A Python framework that automates expert decisions in environmental time-series causal discovery

Environmental time-series causal discovery requires expert decisions about method choice, conditional-independence tests, lag horizons, sample-size adequacy, multiple-testing control, and evidence interpretation. Applied inconsistently across datasets, these choices yield graphs that cannot be compared, reproduced, or audited. We present AutoCause, an open-source Python workflow that records each decision, derives defaults from an extended causal-audit module, and admits domain-informed overrides. The workflow wraps four established causal-discovery methods from three families, adds non-causal reference models, and grades links by method-count support. On 145 datasets from DGP-Atlas, TimeGraph, and a topology-derived CausalRivers reference, the methods recover complementary parts of the reference graphs. Majority-supported links are more precise than single-method links on the synthetic benchmarks but not against river topology. AutoCause converts inconsistent expert practice into an auditable, repeatable analysis; causal interpretation remains with the analyst. Available at https://github.com/marcoruizrueda/autocause.

Marco Ruiz, Miguel Arana-Catania, David R. Ardila +1

ISR-Lisbon, Instituto Superior Técnico, Av. Rovisco Pais 1, Lisbon, 1049-001, Portugal · Digital Scholarship at Oxford, University of Oxford, Oxford, OX1 3BG, United Kingdom · Jet Propulsion Lab., Caltech, Pasadena, CA 91109, California, USA

Time-Series Causal Discovery Causal Discovery Scientific Workflow Automation

Jul 30, 2026cs.CL

Causal Discovery with Inverted Self-attention for Multivariate Time Series

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Yusen Liu, Yong Wang, Yifan Yin +3

School of Computer Science, University of Technology Sydney, Sydney, Australia · TianFu YongXing Laboratory, Chengdu, China · Faculty of Data Science, City University of Macau, Macau, China +1

Time-Series Causal Discovery Causal Discovery Time Series Transformers

Jul 29, 2026cs.LG

DoTime: A Synthetic Benchmark Generator for Interventional and Counterfactual Time Series

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce \textbf{DoTime}, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention \emph{windows}, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks \emph{inside} the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of

100{,}000

trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

Dennis Thumm, Billy Tim Anthony, Ying Chen

National University of Singapore, Singapore, Singapore

Counterfactual Evaluation Structural Causal Models Time-Series Causal Discovery Causal Counterfactual Generation Synthetic Benchmark Generation Causal Intervention

Jul 27, 2026cs.LG

Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series

We describe Causal-TS, an open-source Python library for causal discovery in high-dimensional and nonstationary multivariate time series. Causal-TS provides four specialized algorithms-CDNOTS, CDNOTS+, CEDAR, and GRACE-along with wrappers for GES, Granger, LASSO-VAR, and LGES, all sharing a unified conditional independence (CI) test layer with GPU acceleration via PyTorch. A regime discovery pipeline detects structural breaks via pluggable changepoint detectors and runs discovery per regime with regime-specific parameters. A command-line interface, synthetic data generators, and optional DoWhy integration provide an end-to-end pipeline from raw time series to causal effect estimates. The library is pip-installable, tested on Python 3.10--3.12, and available at https://github.com/bloomberg/causal-ts.

Mohammad Fesanghary

Bloomberg LP, New York, NY, USA

Time-Series Causal Discovery Causal Discovery Causal Inference Conditional Independence Testing

Jul 22, 2026cs.LG

CEDAR: Causal Edge Discovery for Autoregressive Processes

We propose CEDAR (Causal Edge Discovery for Autoregressive Processes), a constraint-based method for lagged causal edge discovery in sparse autoregressive time series. CEDAR screens candidate cross-variable lags using AR(1)-residualized, U-centered distance correlation, then applies two targeted conditional-independence tests per significant cross-variable lag candidate and accepts at most one lag per ordered pair. A stable MCI pruning step removes indirect edges, and optional deterministic C-nodes adjust for specified trend-like nonstationarity. In sparse regimes where few lags survive screening, CEDAR requires

O(d^2)

CI tests after screening while retaining edge-level interpretability. CEDAR is most effective when data are scarce and variables exhibit lag-1 self-dynamics; methods with richer conditioning sets become preferable as

T

grows or when higher-order autoregressive or simultaneous multi-lag effects are common.

Mohammad Fesanghary

Bloomberg LP

Time-Series Causal Discovery Causal Discovery Autoregressive Modeling

Jul 20, 2026cs.LG

Causal Discovery on Irregular Time Series

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

Martim Penim, Ricardo Ribeiro Pereira, Jacopo Bono +3

1Feedzai, Portugal · 3DCC, Faculdade de Ciêncidas da Universidade do Porto, Portugal · 2Instituto Superior Técnico, Universidade de Lisboa, Portugal +1

Irregular Time-Series Modeling Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Jun 22, 2026cs.LG

GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series

From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE (

\textbf{G}

ated

\textbf{R}

efinement for

\textbf{A}

ccurate

\textbf{C}

ausal

\textbf{E}

dge discovery), which refines constraint-based discovery using Hard Concrete gates with

L_0

regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by

L_1

and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to

d=100

, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost (

75\times

faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive (

F_1 = 0.86

, AUROC

{} = 0.99

), reducing the skeleton's 106 false positives by 99%.

Mohammad Fesanghary, Abhinav Havaldar

Time-Series Causal Discovery Causal Discovery Causal Inference

Jun 18, 2026cs.LG

Temporal Causal Prior-Data Fitted Networks for Panel Data with Learned Reliability Signals

Estimating causal effects in industrial time series requires handling temporal dynamics, time-varying treatments, and unobserved confounders. Existing causal foundation models (CausalPFN, CausalFM) operate only on static cross-sectional data; neural temporal methods (CRN, G-Net) require per-dataset training; and concurrent temporal-PFN proposals have not been demonstrated at industrial scale. None output explicit per-pair reliability signals alongside their CATE estimates. We introduce Temporal Causal Prior-Data Fitted Networks (TCPFN), a foundation model for zero-shot temporal causal discovery with learned reliability signals. TCPFN makes four contributions: (1) a Causal Judgment Head that jointly predicts null-effect probability, confounding strength, identifiability, mediation fraction, and causal regime; (2) a mixed training prior covering six causal regimes (independent, direct, confounded, mediated, time-varying confounded, feedback) plus CausalFM-style front-door and instrumental-variable priors; (3) a discrete-token panel-data architecture with cross-attention masking that prevents inter-horizon leakage; (4) zero-shot inference at industrial scale via FAISS-based context selection and one-step posterior correction. On 19 benchmark datasets across five domains, TCPFN achieves competitive zero-shot causal discovery: AUROC 0.96 on Tennessee Eastman, 0.93 on SWaT, 0.98 on Causal Rivers, 0.97 on CAUSRCA. The null detector reaches NullF1 0.94, AUROC 0.99. TCPFN scales to V=1,275 on a proprietary Kraft pulp-and-paper dataset in 6 hours on a single GPU; PCMCI, a CPU-only library, on a V=666 sub-panel of the same data took 81.5 hours, extrapolating by O(V^2) to ~12.5 days at V=1,275. TCPFN's top edges identify cross-subsystem causal relationships while PCMCI's surface within-instrument controller-measurement coupling -- a scalability case study.

Shravan Talupula, Saurabh Sharma

ProfitOps Inc.

Causal Foundation Models Causal Effect Estimation Time-Series Causal Discovery Causal Identifiability Prior-Data Fitted Networks Causal Discovery with Latent Confounding

Jun 11, 2026cs.NI

Graphical Causal Reasoning for Root Cause Analysis in Cloud Networks

Cloud-computing relies on large-scale networks which are inherently complex systems. In this paper, we present a novel approach to root cause analysis (RCA) of cloud network incidents, leveraging graph-based causal discovery techniques. Our method addresses the limitations of rule-based automation by introducing a spatiotemporal grouping strategy and an automation ontology to reduce the dimensionality of the problem. We construct a causal graph from binary time series data using bivariate Granger causality and conditional independence tests. For inference, we introduce a probabilistic method that assigns edge-specific conditional probabilities as a function of time lag, allowing for interpretable, time-aware root cause scoring via causal graph traversal. We evaluated the system using a labeled dataset of 35 production incidents from a major cloud provider. The model successfully recalled the correct root cause in 85.7% of incidents and produced an exact match in 74.3%. In production, the deployed system has been used in over 800 real-world incidents, with positive qualitative feedback from network engineers. These results highlight the practicality of a data-driven, causal approach to RCA in dynamic and large-scale operational environments.

Fabien Chraim, Dominik Janzing, John Evans

Amazon Web Services

Time-Series Causal Discovery Cloud Computing Causal Reasoning Root Cause Analysis

Jun 11, 2026cs.LG

CausalMoE: A Billion-Scale Multimodal Foundation Model for Granger Causal Discovery with Pattern-Routed Heterogeneous Experts

Granger Causal Discovery (GCD) is fundamental for analyzing temporal dependencies in complex systems. However, existing neural GCD methods predominantly rely on a "one-size-fits-all" paradigm, struggling to capture distribution shifts and dynamic regime changes inherent in real-world time series. This often leads to entangled representations and spurious causal graphs. In this paper, we propose CausalMoE, a billion-scale multimodal Granger causal foundation model that explicitly models patch-level heterogeneity. CausalMoE introduces a Pattern-Routed Mixture of Heterogeneous Experts, which dynamically identifies latent temporal patterns and routes patches to specialized domain experts, effectively decoupling regime-specific mechanisms from shared dynamics. To ensure interpretable graph recovery, we design a Causality-Aware Self-Attention mechanism operating across variables, yielding sparse Granger causal graphs via proximal optimization. Furthermore, CausalMoE is the first to integrate LLMs and VLMs to align numerical signals with textual and visual priors, regularizing causal estimation in complex scenarios. Extensive experiments demonstrate that CausalMoE establishes a new state-of-the-art on fully supervised benchmarks, while effectively generalizing to few-shot settings where traditional methods fail.

Bo Liu, Di Dai, Jingwei Liu +5

State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University Beijing, China · National Institute of Health Data Science, and Institute for Artificial Intelligence, Peking University Beijing, China

Time-Series Causal Discovery Mixture-of-Experts Models Time-Series Foundation Models

Jun 2, 2026cs.LG

Learning Temporal Causal Structure via Smooth Differentiable Optimization

Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.

Tong Zhao, Ce Guo, Wayne Luk +2

Time-Series Causal Discovery Causal Discovery

Jun 1, 2026stat.ML

Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families

Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.

Roel Hulsman, Carles Balsells-Rodas, Sara Magliacane

University of Amsterdam · 2Adyen · 3Imperial College London +1

Time-Series Causal Discovery Regime-Switching Dynamical Systems Causal Structure Learning Causal Identifiability Non-Stationary Time Series

May 26, 2026cs.LG

Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretraining

Causal discovery from time series is critical for many real-world applications, such as tracing the root causes of anomalies. Existing approaches typically rely on dataset-specific optimization, making it difficult to transfer their causal discovery capabilities to new time series governed by diverse causal mechanisms. In this paper, we propose \textbf{PTCD}, a novel \textbf{P}retraining framework for \textbf{T}ime-series \textbf{C}ausal \textbf{D}iscovery, which improves cross-task generalization through context-conditioned modeling and transferable causal augmentation. To model complex temporal causal dependencies, PTCD employs a dual-scale iterative attention mechanism to capture window-level causal relationships, and a Gaussian mixture with a context-level routing mechanism to handle heterogeneous exogenous distributions. To further address distribution shifts across causal graphs, PTCD adopts a pretraining paradigm on synthetic datasets that integrates intervention-based learning and a causal mixup strategy, promoting stable causal discovery and stronger generalization. Extensive experiments on multiple real-world out-of-distribution (OOD) datasets demonstrate that PTCD excels in both causal discovery and root cause identification.

Biao Ouyang, Tengxue Zhang, Zhihao Zhuang +3

East China Normal University

Time-Series Causal Discovery OOD Generalization Root Cause Analysis

May 26, 2026cs.CR

Certified Causal Attribution for Real-Time Attack Forensics in 6G Network Slicing

Cross-slice attack attribution in 6G networks requires identifying causal propagation chains through shared infrastructure in under 100 ms. Existing methods struggle to satisfy this strict SLA without sacrificing accuracy, because shared resource contention creates spurious correlations that are indistinguishable from genuine causal links under standard Granger tests. We propose DA-GC, a certified causal attribution framework that integrates resource-conditioned Granger causality with an axiomatically derived Resource Contention Model (RCM) to systematically block resource-mediated confounding. On a 15-slice production-emulation 6G testbed with 1,100 attack scenarios, DA-GC achieves 89.2% attribution accuracy at 87 ms. This represents a 7.9 percentage-point improvement over the strongest baseline at 2.7x lower latency, alongside demonstrated cross-topology generalization and concept-drift resilience. Crucially, DA-GC is backed by a comprehensive formal certification stack. We provide mathematically proven validity certificates for statistical soundness under serially dependent telemetry and piecewise-stationarity. Furthermore, we establish strict security bounds, including an adversarial utilization spoofing breakdown point of

δ^* \approx 0.95

, and define the minimum differential-privacy noise required for a provably private and robust deployment.

Minh K. Quan, Pubudu N. Pathirana

School of Engineering, Deakin University, Geelong VIC 3220, Australia

6G Networks Time-Series Causal Discovery Cybersecurity Causal Attribution Wireless Communications

May 26, 2026cs.LG

Function-Valued Causal Influence in Nonlinear Time Series

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.

Valentina V. Kuskova, Dmitry Zaytsev, Michael Coppedge

Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, Indiana, USA. · Department of Political Science, University of Notre Dame, Notre Dame, Indiana, USA.

Causal Effect Estimation Time-Series Causal Discovery

May 21, 2026stat.ME

Causal Discovery in Structural VAR Models Under Equal Noise Variance

Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling rate may be coarse relative to the underlying dynamics and contemporaneous effects need not form an acyclic graph. We study causal discovery in linear Gaussian structural VAR models under an equal noise variance assumption, meaning that the structural noise terms have a common variance. Unlike the DAG-based cross-sectional equal noise variance setting, the time-series setting considered here does not generally yield point identification of a unique causal graph. Instead, multiple structural VAR parameterizations can induce the same stationary observed process law. We introduce a notion of observational equivalence tailored to this setting and show that the corresponding equivalence class is characterized by orthogonal transformations of the structural equations together with a global positive scale. This characterization leads to an equivalence-aware model discrepancy, the observational alignment discrepancy, which compares structural models modulo transformations that preserve the observed law. Building on this theory, we propose ENVAR, a sparsity-based procedure that searches over the induced observational equivalence class for a sparse normalized structural representative. We evaluate the proposed methodology on synthetic structural VAR data and on an fMRI dataset.

SeyedSina Seyedi HasanAbadi, Fahimeh Arab, Erfan Nozari +1

Bourns College of Engineering, University of California, Riverside · University of California, San Francisco · Department of Mathematics and Statistics, Boston University

Time-Series Causal Discovery Causal Discovery Causal Identifiability Autoregressive Modeling

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.LG

Prediction Bottlenecks Don't Discover Causal Structure (But Here's What They Actually Do)

A Mamba state-space model trained only for next-step prediction appears to recover Granger-causal structure through a simple readout

S = |W_{out} W_{in}|

, with early experiments suggesting the phenomenon generalized across architectures and benefited from interventional data at

p < 10^{-5}

. We package the protocol used to test that claim -- standardized synthetic generators (VAR/Lorenz/CauseMe-style), three intervention semantics (

do(X=c)

, soft-noise, random-forcing), edge-provenance cards on three real datasets, and size-matched control arms -- as a reusable falsification benchmark, and walk the claim through it in five stages. The method-level claim does not survive: (i) a plain linear bottleneck does as well or better; (ii) tuned Lasso beats the bottleneck on synthetic CauseMe-style benchmarks, and on Lorenz-96 (the only real benchmark with unambiguous ground truth) classical PCMCI and Granger lead a tight cluster in which the bottleneck trails; (iii) the headline intervention advantage is roughly 60% a sample-size confound, and the residual disappears under standard

do(X=c)

interventions, surviving only under a non-standard random-forcing scheme; (iv) even that residual reproduces, with a larger effect, in classical bivariate Granger -- the effect is method-agnostic. What survives is a narrow characterization result; the benchmark is the lasting artifact, and each stage above is one of its control arms.

Ankit Hemant Lade, Sai Krishna Jasti, Indar Kumar +1

Time-Series Causal Discovery Causal Discovery

May 8, 2026cs.LG

Mask2Cause: Causal Discovery via Adjacency Constrained Causal Attention

Leveraging deep learning for causal discovery in time series remains challenging because existing neural methods predominantly rely on component-wise architectures that fail to capture shared system dynamics or employ decoupled post-hoc graph extraction that risks overfitting to spurious correlations. We propose

\textbf{Mask2Cause}

, an end-to-end framework that recovers the underlying causal graph directly during the forecasting forward pass. Our approach introduces an Inverted Variable Embedding and an Adjacency-Constrained Masked Attention mechanism, trained with homoscedastic or heteroscedastic objectives to capture causal influences in both mean and variance. Empirical results on diverse benchmarks, from synthetic chaotic dynamics to realistic biological simulations, demonstrate state-of-the-art causal discovery with significantly reduced parameter complexity compared to standard baselines. We further show that inferred causal structures can be used to reduce parameter count of forecasting models by more than 70% on average while maintaining predictive accuracy.

Omar Muhammad, Pasupuleti Dhruv Shivkant, Deepak N. Subramani

1Indian Institute of Science, Bengaluru, India

Time-Series Causal Discovery Causal Structure Learning

May 8, 2026cs.LG

PerCaM-Health: Personalized Dynamic Causal Graphs for Healthcare Reasoning

Personalized healthcare decisions require reasoning about how physiological and behavioral variables influence an individual patient over time. Existing temporal causal discovery methods are poorly matched to this setting: cohort-level models provide stable but non-personalized structures, while per-patient discovery is unreliable because individual trajectories are short, noisy, irregular, and non-stationary. This creates a fundamental gap between population-level causal modeling and the patient-specific, time-varying mechanisms needed for intervention reasoning. We introduce PerCaM-Health, a framework for learning personalized dynamic causal graphs from longitudinal health data. The framework learns a knowledge-guided population temporal graph, then conservatively adapts and evolves it using patient-specific temporal evidence and rolling-window updates, producing interpretable and auditable graph sequences. By coupling these graphs with temporal structural equations, the framework enables patient-level counterfactual queries, such as estimating short-horizon outcome changes under hypothetical behavioral interventions. Experiments on a semi-synthetic dynamic health benchmark show that PerCaM-Health improves graph recovery, dynamic edge tracking, and intervention direction accuracy compared to cohort-level, per-patient, and non-personalized temporal baselines. These results demonstrate that jointly modeling personalization and temporal evolution yields more reliable causal structure and intervention reasoning.

Elahe Khatibi, Ziyu Wang, Saba A. Farahani +4

University of California, Irvine · Washington University in St. Louis

Structural Causal Models Healthcare Time-Series Causal Discovery Causal Discovery Causal Structure Learning Clinical Reasoning+1

May 4, 2026cs.LG

TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations

Causal Discovery (CD) is a powerful framework for scientific inquiry. Yet, its practical adoption is hindered by a reliance on strong, often unverifiable assumptions and a lack of robust performance assessment. To address these limitations and advance empirical CD evaluation, we present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications. With this, we strive to ultimately facilitate the development of CD methods that are reliable for a diverse range of synthetic and potentially real-world data conditions.

Gideon Stein, Niklas Penzel, Tristan Piater +1

Computer Vision Group Jena Friedrich Schiller University Jena Jena, Thuringia, 07743, DE

Time-Series Causal Discovery Causal Discovery

May 3, 2026stat.ML

PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery

External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable -- physical laws are trustworthy, LLM-suggested edges are speculative -- yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware

\ell_1

and prior-weighted

\ell_2

regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is

\varepsilon

-safe in expectation over the prior-generation distribution, with

\varepsilon\leq C\cdot\mathrm{acc}(1{-}\mathrm{acc})\cdot d^2/T

at the parametric

T^{-1}

rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain

+0.067/+0.089

AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead

+0.123/+0.043

over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at

d{=}300

; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched

W_0

-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.

Xihang Shan, Da Zhou

School of Mathematical Sciences Xiamen University Fujian, China

Time-Series Causal Discovery Bayesian Inference Causal Discovery

May 1, 2026cs.AI

To Use AI as Dice of Possibilities with Timing Computation

The dominant noun-based modeling paradigm, grounded in probability theory and committed to pre-specified noun entities as primitive modeling units, is insufficient as a \emph{grammar of thought}: It leaves \emph{timing} outside the computational scope, precluding any adequate representation of the future as an open space of possibilities. This paper addresses three conceptual gaps absent from the existing literature: (1) possibility space -- a framework admitting multiple possible timelines for the same event; (2) timing computation -- the treatment of timing as a computable rather than observed dimension; and (3) causal factum -- the maximal causal efficacy recovered by reasoning backward from possible futures, rather than assumed in advance. Together, these definitions dissolve the confounding problem inherent to noun-based causal inference and provide the foundation for a spontaneously growing causal-reasoning world model. As proof of concept, we instantiate the framework and apply it to longitudinal EHR data from 3,276 breast cancer patients, demonstrating for the first time, to our knowledge, automatic trajectory discovery and counterfactual timing deduction (i.e., a What-If Machine) in a purely data-driven manner.

Jia Li, Vipin Kumar, Rui Zhang

Department of Surgery, University of Minnesota, Minneapolis, United States · Department of Computer Science & Engineering, University of Minnesota, Minneapolis, United States

Causal World Models Time-Series Causal Discovery Causal Reasoning Counterfactual Reasoning