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arxiv: 2602.13004 · v2 · submitted 2026-02-13 · 💻 cs.LG · stat.ML

Towards Uncertainty-Aware Federated Granger Causal Learning

Ayush Mohanty , Nazal Mohamed , Nagi Gebraeel This is my paper

Pith reviewed 2026-05-15 22:28 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords federated learninggranger causalityuncertainty quantificationcausal discoverydistributed time serieshypothesis testingvariance propagationstructure learning
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The pith

Federated Granger causality uncertainty depends only on client data statistics, independent of model priors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops uncertainty tracking for Granger causality when time-series data is vertically partitioned across clients, so each sees only its own variables. It derives closed-form recursions for how covariance propagates through the client-server exchanges and proves convergence to steady-state variances under spectral-radius stability conditions. The key result is that these final variances are fixed entirely by the statistics of each client's observed data and do not change with different priors on the model parameters. This characterization supports a post-training test that flags genuine cross-client causal links versus those induced by noise. The finding matters for any distributed monitoring task where operators must decide which inferred interactions are reliable enough to act on.

Core claim

Under mild stability conditions, the steady-state uncertainty in federated Granger causal learning depends only on client data statistics and is independent of the priors placed on the model parameters. The authors derive closed-form covariance recursions for the cross-covariances induced by the coupled client-server feedback loop and establish spectral-radius-based convergence conditions yielding closed-form expressions for the steady-state variances at both the client and server. A hypothesis-testing procedure built on these expressions separates genuine cross-client interactions from spurious edges.

What carries the argument

Closed-form covariance recursions for cross-covariances in the coupled client-server feedback loop together with spectral-radius convergence conditions that produce explicit steady-state variance formulas.

If this is right

  • Uncertainty can be computed from client data statistics alone once the loop stabilizes.
  • A post-training hypothesis test can reliably separate genuine cross-client causal edges from noise-induced ones.
  • The predicted variances match observed behavior across multiple operating regimes in experiments.
  • The approach outperforms existing federated causal structure learning baselines on both synthetic and real datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same variance formulas could be reused in other federated time-series estimation tasks that involve similar client-server coupling.
  • In stable systems, designers can de-emphasize prior tuning because it does not affect long-run uncertainty.
  • Real-time operators could threshold actions on cross-client links using the closed-form variances rather than heuristic confidence scores.
  • The stability conditions point to a practical design rule: communication schedules should be chosen to keep the feedback-loop spectral radius safely below one.

Load-bearing premise

The coupled client-server feedback loop satisfies spectral-radius conditions that guarantee convergence to the derived steady-state variances.

What would settle it

Fix the client data and rerun the federated procedure with materially different priors on the model parameters; if the observed steady-state variances change, the claim that uncertainty depends only on data statistics is falsified.

Figures

Figures reproduced from arXiv: 2602.13004 by Ayush Mohanty, Nagi Gebraeel, Nazal Mohamed.

Figure 1
Figure 1. Figure 1: Uncertainty prop. during training for different levels of [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Uncertainty prop. for different levels of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Uncertainty prop. for different levels of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Trace of the covariance for off-diagonal blocks of the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trace of the covariance for each off-diagonal block of the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Nonlinear Exper. on HAI: Trace of the covariance for the off-diagonal blocks of the Jacobian matrix [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of DP Gaussian noise on steady-state uncertainty and causal link detection in the synthetic dataset. [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Uncertainty propagation in the cross-covariance terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Uncertainty propagation in the cross-covariance terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p032_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Uncertainty propagation in the cross-covariance terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p032_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Uncertainty propagation in the communicated terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p032_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Uncertainty propagation in the communicated terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p033_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Uncertainty propagation in the communicated terms during FedGC learning for different regimes of [PITH_FULL_IMAGE:figures/full_fig_p033_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Average L2 norm error of each off-diagonal block of the matrix A for different regimes of Σ t ym for HAI dataset 0 5000 10000 15000 20000 25000 30000 Number of iterations 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 k µ ˆAt12 − A12 k 2 Σ 0 Aˆmn ∼ 10−6 Σ 0 Aˆmn ∼ 10−4 Σ 0 Aˆmn ∼ 10−2 Σ 0 Aˆmn ∼ 100 (a) ∥µAˆt 12 − A12∥2 0 5000 10000 15000 20000 25000 30000 Number of iterations 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 k µ… view at source ↗
Figure 15
Figure 15. Figure 15: Average L2 norm error of each off-diagonal block of the matrix A for different regimes of Σ 0 Aˆmn for HAI dataset 34 [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Nonlinear Exper. on HAI: Trace of the covariance for the off-diagonal blocks of the Jacobian matrix [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Trace of the covariance for each off-diagonal block of the [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Average L2 norm error of each off-diagonal block of the 5 × 5 matrix A for different regimes of Σ t ym on SWaT dataset 37 [PITH_FULL_IMAGE:figures/full_fig_p037_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Trace of the covariance for each off-diagonal block of the [PITH_FULL_IMAGE:figures/full_fig_p038_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Average L2 norm error of each off-diagonal block of the A matrix for different regimes of Σ 0 Aˆmn on SWaT dataset 39 [PITH_FULL_IMAGE:figures/full_fig_p039_20.png] view at source ↗
read the original abstract

Granger causality recovers directed interactions from time-series data, but in many distributed systems, the data are vertically partitioned across clients, with each client observing only the variables of its own subsystem. Federated Granger causality (FedGC) recovers cross-client interactions without sharing raw data. Existing FedGC methods, however, return deterministic point estimates with no calibrated measure of uncertainty, leaving operators without a principled basis for identifying reliable cross-client interactions. We address this limitation by characterizing how uncertainty propagates through the FedGC framework. We derive closed-form covariance recursions for the cross-covariances induced by the coupled client-server feedback loop, and establish spectral-radius-based convergence conditions yielding closed-form expressions for the steady-state variances at both the client and server. Under mild stability conditions, we prove that the steady-state uncertainty depends only on client data statistics (aleatoric) and is independent of the priors placed on the model parameters (epistemic). Building on this asymptotic characterization, we construct a post-training hypothesis testing procedure that separates genuine cross-client interactions from spurious edges. Experiments on synthetic and real-world datasets show that the predicted uncertainty propagation matches the theory across multiple operating regimes, while consistently outperforming the state-of-the-art federated causal structure learning baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops an uncertainty-aware approach to federated Granger causal learning (FedGC). It derives closed-form recursions for the covariance of the parameter estimates induced by the client-server interaction, establishes spectral-radius conditions for convergence to steady-state variances, and proves that under these conditions the steady-state uncertainty is determined solely by the aleatoric noise statistics of the client data and is independent of the epistemic priors on the VAR coefficients. A post-training hypothesis test is constructed to distinguish genuine cross-client Granger edges from spurious ones, with validation on synthetic and real-world datasets.

Significance. If the central theoretical claims hold, the work would be significant for federated causal discovery by providing calibrated uncertainty estimates that separate aleatoric and epistemic components without requiring raw data sharing. The explicit derivation of the covariance recursions and the asymptotic independence result represent a clear advance over existing deterministic FedGC methods. Empirical matches between predicted and observed variances across regimes strengthen the contribution.

major comments (2)
  1. The claim that steady-state uncertainty is independent of priors rests on the decay of the homogeneous solution to the covariance recursion. The manuscript invokes 'mild stability conditions' but does not provide an explicit expression for the closed-loop matrix whose spectral radius must be less than one, nor does it verify that this radius remains strictly below one when cross-client edges are admitted.
  2. The hypothesis testing procedure for separating genuine from spurious edges is built on the derived steady-state variances; however, the finite-sample behavior of the test statistic under the federated updates is not analyzed, leaving open whether the asymptotic variances provide reliable p-values in moderate data regimes.
minor comments (2)
  1. The legend and axis labels in the variance comparison plots could be clarified to distinguish between theoretical predictions and empirical estimates more explicitly.
  2. The distinction between client-local and server-aggregated quantities is sometimes ambiguous in the recursion definitions; a table summarizing the symbols would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment point by point below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: The claim that steady-state uncertainty is independent of priors rests on the decay of the homogeneous solution to the covariance recursion. The manuscript invokes 'mild stability conditions' but does not provide an explicit expression for the closed-loop matrix whose spectral radius must be less than one, nor does it verify that this radius remains strictly below one when cross-client edges are admitted.

    Authors: We agree that the explicit form of the closed-loop matrix improves rigor. In the revised manuscript we will state the matrix explicitly: it is the Kronecker product (A ⊗ A) composed with the federated averaging operator, where A is the block-structured VAR coefficient matrix that already incorporates any cross-client edges. The spectral-radius condition is therefore identical to the stability of the underlying joint VAR process; because cross-client edges are part of this joint process, the radius remains strictly below one whenever the overall time series is stable (a standard assumption already used in the paper). We will add the explicit matrix expression to Section 3.2 and a short verification paragraph to the appendix. revision: yes

  2. Referee: The hypothesis testing procedure for separating genuine from spurious edges is built on the derived steady-state variances; however, the finite-sample behavior of the test statistic under the federated updates is not analyzed, leaving open whether the asymptotic variances provide reliable p-values in moderate data regimes.

    Authors: We acknowledge that a full finite-sample analysis of the test statistic is absent. The current experiments already show close agreement between predicted and observed variances for moderate sample sizes (N = 500–2000) across multiple regimes, and the hypothesis test is applied directly to these regimes. In the revision we will add (i) a brief discussion of the exponential convergence rate of the covariance recursion and (ii) supplementary simulations that report empirical type-I error rates and power of the post-training test for varying N. A rigorous non-asymptotic bound on the test statistic remains outside the scope of this work. revision: partial

Circularity Check

0 steps flagged

Derivation of steady-state uncertainty is self-contained from update equations

full rationale

The covariance recursions are obtained directly from the client-server update equations, and the independence of the steady-state variances from epistemic priors follows from the asymptotic decay of the homogeneous solution under the assumed spectral-radius condition. No step reduces a prediction or central claim to a fitted parameter, self-citation, or definitional tautology; the result is independent of the target data statistics beyond the stated noise covariances.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a stable feedback loop whose spectral radius is less than one, allowing the covariance recursions to converge to a unique steady state determined by client data moments.

axioms (1)
  • domain assumption The client-server feedback loop satisfies spectral-radius-based convergence conditions
    Invoked to guarantee that steady-state variances exist and are independent of initial priors.

pith-pipeline@v0.9.0 · 5516 in / 1168 out tokens · 20889 ms · 2026-05-15T22:28:33.604492+00:00 · methodology

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

  1. [1]

    Granger causality: A review and recent advances.Annual Review of Statistics and Its Application, 9(1):289–319, 2022

    Ali Shojaie and Emily B Fox. Granger causality: A review and recent advances.Annual Review of Statistics and Its Application, 9(1):289–319, 2022

    work page 2022

  2. [2]

    Large-scale nonlinear granger causality for inferring directed dependence from short multivariate time-series data.Scientific reports, 11(1):7817, 2021

    Axel Wism¨uller, Adora M Dsouza, M Ali V osoughi, and Anas Abidin. Large-scale nonlinear granger causality for inferring directed dependence from short multivariate time-series data.Scientific reports, 11(1):7817, 2021

    work page 2021

  3. [3]

    Neural granger causality.IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(8):4267–4279, 2021

    Alex Tank, Ian Covert, Nicholas Foti, Ali Shojaie, and Emily B Fox. Neural granger causality.IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(8):4267–4279, 2021

    work page 2021

  4. [4]

    Federated granger causality learning for interdependent clients with state space representation.International conference on learning representations, 2025

    Ayush Mohanty, Nazal Mohamed, Paritosh Ramanan, and Nagi Gebraeel. Federated granger causality learning for interdependent clients with state space representation.International conference on learning representations, 2025

    work page 2025

  5. [5]

    Gradient-based uncertainty attribution for explainable bayesian deep learning

    Hanjing Wang, Dhiraj Joshi, Shiqiang Wang, and Qiang Ji. Gradient-based uncertainty attribution for explainable bayesian deep learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12044–12053, 2023

    work page 2023

  6. [6]

    Enabling uncertainty estimation in iterative neural networks.arXiv preprint arXiv:2403.16732, 2024

    Nikita Durasov, Doruk Oner, Jonathan Donier, Hieu Le, and Pascal Fua. Enabling uncertainty estimation in iterative neural networks.arXiv preprint arXiv:2403.16732, 2024

    work page arXiv 2024

  7. [7]

    A survey of uncertainty in deep neural networks.Artificial Intelligence Review, 56(Suppl 1):1513–1589, 2023

    Jakob Gawlikowski, Cedrique Rovile Njieutcheu Tassi, Mohsin Ali, Jongseok Lee, Matthias Humt, Jianxiang Feng, Anna Kruspe, Rudolph Triebel, Peter Jung, Ribana Roscher, et al. A survey of uncertainty in deep neural networks.Artificial Intelligence Review, 56(Suppl 1):1513–1589, 2023

    work page 2023

  8. [8]

    Estimating epistemic and aleatoric uncertainty with a single model.Advances in Neural Information Processing Systems, 37:109845–109870, 2024

    Matthew Chan, Maria Molina, and Chris Metzler. Estimating epistemic and aleatoric uncertainty with a single model.Advances in Neural Information Processing Systems, 37:109845–109870, 2024

    work page 2024

  9. [9]

    Separation of aleatoric and epistemic uncertainty in deterministic deep neural networks

    Denis Huseljic, Bernhard Sick, Marek Herde, and Daniel Kottke. Separation of aleatoric and epistemic uncertainty in deterministic deep neural networks. In2020 25th International Conference on Pattern Recognition (ICPR), pages 9172–9179. IEEE, 2021

    work page 2021

  10. [10]

    The unreasonable effectiveness of deep evidential regression

    Nis Meinert, Jakob Gawlikowski, and Alexander Lavin. The unreasonable effectiveness of deep evidential regression. InProceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 9134–9142, 2023

    work page 2023

  11. [11]

    Quantifying aleatoric and epistemic uncertainty: A credal approach

    Paul Hofman, Yusuf Sale, and Eyke H ¨ullermeier. Quantifying aleatoric and epistemic uncertainty: A credal approach. InICML 2024 Workshop on Structured Probabilistic Inference{\&}Generative Modeling, 2024

    work page 2024

  12. [12]

    Aleatoric and epistemic uncertainty in machine learning: An introduc- tion to concepts and methods.Machine learning, 110(3):457–506, 2021

    Eyke H¨ullermeier and Willem Waegeman. Aleatoric and epistemic uncertainty in machine learning: An introduc- tion to concepts and methods.Machine learning, 110(3):457–506, 2021

    work page 2021

  13. [13]

    Bayesian nonparametric federated learning of neural networks

    Mikhail Yurochkin, Mayank Agarwal, Soumya Ghosh, Kristjan Greenewald, Nghia Hoang, and Yasaman Khazaeni. Bayesian nonparametric federated learning of neural networks. InInternational conference on machine learning, pages 7252–7261. PMLR, 2019

    work page 2019

  14. [14]

    Fedpop: A bayesian approach for personalised federated learning.Advances in Neural Information Processing Systems, 35:8687–8701, 2022

    Nikita Kotelevskii, Maxime V ono, Alain Durmus, and Eric Moulines. Fedpop: A bayesian approach for personalised federated learning.Advances in Neural Information Processing Systems, 35:8687–8701, 2022

    work page 2022

  15. [15]

    Personalized federated learning via variational bayesian inference

    Xu Zhang, Yinchuan Li, Wenpeng Li, Kaiyang Guo, and Yunfeng Shao. Personalized federated learning via variational bayesian inference. InInternational Conference on Machine Learning, pages 26293–26310. PMLR, 2022

    work page 2022

  16. [16]

    Fedbe: Making bayesian model ensemble applicable to federated learning

    Hong-You Chen and Wei-Lun Chao. Fedbe: Making bayesian model ensemble applicable to federated learning. arXiv preprint arXiv:2009.01974, 2020

    work page arXiv 2009

  17. [17]

    Federated learning for indoor localization via model reliability with dropout.IEEE Communications Letters, 26(7):1553– 1557, 2022

    Junha Park, Jiseon Moon, Taekyoon Kim, Peng Wu, Tales Imbiriba, Pau Closas, and Sunwoo Kim. Federated learning for indoor localization via model reliability with dropout.IEEE Communications Letters, 26(7):1553– 1557, 2022

    work page 2022

  18. [18]

    Federated machine learning: Concept and applications

    Qiang Yang, Yang Liu, Tianjian Chen, and Yongxin Tong. Federated machine learning: Concept and applications. ACM Transactions on Intelligent Systems and Technology (TIST), 10(2):1–19, 2019

    work page 2019

  19. [19]

    Vertibayes: learning bayesian network parameters from vertically partitioned data with missing values.Complex & Intelligent Systems, 10(4):5317–5329, 2024

    Florian Van Daalen, Lianne Ippel, Andre Dekker, and Inigo Bermejo. Vertibayes: learning bayesian network parameters from vertically partitioned data with missing values.Complex & Intelligent Systems, 10(4):5317–5329, 2024

    work page 2024

  20. [20]

    Distributed federated kalman filter fusion over multi-sensor unreliable networked systems.IEEE Transactions on Circuits and Systems I: Regular Papers, 63(10):1714–1725, 2016

    Zirui Xing and Yuanqing Xia. Distributed federated kalman filter fusion over multi-sensor unreliable networked systems.IEEE Transactions on Circuits and Systems I: Regular Papers, 63(10):1714–1725, 2016

    work page 2016

  21. [21]

    Federated kalman filter for secure iot-based device monitoring services

    Marc Jayson Baucas and Petros Spachos. Federated kalman filter for secure iot-based device monitoring services. IEEE Networking Letters, 5(2):91–94, 2023. 12 PREPRINT

    work page 2023

  22. [22]

    A distributed multiarea state estimation.IEEE Transactions on Power Systems, 26(1):73–84, 2010

    George N Korres. A distributed multiarea state estimation.IEEE Transactions on Power Systems, 26(1):73–84, 2010

    work page 2010

  23. [23]

    A review on distribution system state estimation.IEEE Transactions on Power Systems, 32(5):3875–3883, 2016

    Anggoro Primadianto and Chan-Nan Lu. A review on distribution system state estimation.IEEE Transactions on Power Systems, 32(5):3875–3883, 2016

    work page 2016

  24. [24]

    Federated learning as variational inference: A scalable expectation propagation approach

    Han Guo, Philip Greengard, Hongyi Wang, Andrew Gelman, Yoon Kim, and Eric Xing. Federated learning as variational inference: A scalable expectation propagation approach. InThe Eleventh International Conference on Learning Representations

    work page

  25. [25]

    Federated variational inference: Towards improved personalization and generalization

    Elahe Vedadi, Joshua V Dillon, Philip Andrew Mansfield, Karan Singhal, Arash Afkanpour, and Warren Richard Morningstar. Federated variational inference: Towards improved personalization and generalization. InProceed- ings of the AAAI Symposium Series, volume 3, pages 323–327, 2024

    work page 2024

  26. [26]

    Fedcsl: a scalable and accurate approach to federated causal structure learning

    Xianjie Guo, Kui Yu, Lin Liu, and Jiuyong Li. Fedcsl: a scalable and accurate approach to federated causal structure learning. InProceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 12235– 12243, 2024

    work page 2024

  27. [27]

    Enhancing causal discovery in federated settings with limited local samples

    Xianjie Guo, Liping Yi, Xiaohu Wu, Kui Yu, and Gang Wang. Enhancing causal discovery in federated settings with limited local samples. InInternational Workshop on Trustworthy Federated Learning, pages 164–179. Springer, 2024

    work page 2024

  28. [28]

    Robust aggregation for federated learning.IEEE Transactions on Signal Processing, 70:1142–1154, 2022

    Krishna Pillutla, Sham M Kakade, and Zaid Harchaoui. Robust aggregation for federated learning.IEEE Transactions on Signal Processing, 70:1142–1154, 2022

    work page 2022

  29. [29]

    Byzantine-robust aggregation in federated learning empowered industrial iot.IEEE Transactions on Industrial Informatics, 19(2):1165–1175, 2021

    Shenghui Li, Edith Ngai, and Thiemo V oigt. Byzantine-robust aggregation in federated learning empowered industrial iot.IEEE Transactions on Industrial Informatics, 19(2):1165–1175, 2021

    work page 2021

  30. [30]

    Two ics security datasets and anomaly detection contest on the hil-based augmented ics testbed

    Hyeok-Ki Shin, Woomyo Lee, Jeong-Han Yun, and Byung-Gi Min. Two ics security datasets and anomaly detection contest on the hil-based augmented ics testbed. InCyber Security Experimentation and Test Workshop, CSET ’21, page 36–40, New York, NY , USA, 2021. Association for Computing Machinery

    work page 2021

  31. [31]

    Mathur and Nils Ole Tippenhauer

    Aditya P. Mathur and Nils Ole Tippenhauer. Swat: a water treatment testbed for research and training on ics security. In2016 International Workshop on Cyber-physical Systems for Smart Water Networks (CySWater), pages 31–36, 2016

    work page 2016

  32. [32]

    N4sid: Subspace algorithms for the identification of combined deterministic-stochastic systems.Autom., 30:75–93, 1994

    Peter Van Overschee and Bart De Moor. N4sid: Subspace algorithms for the identification of combined deterministic-stochastic systems.Autom., 30:75–93, 1994

    work page 1994

  33. [33]

    server →client

    Tengfei Ma, Trong Nghia Hoang, and Jie Chen. Federated learning of models pre-trained on different features with consensus graphs. InUncertainty in artificial intelligence, pages 1336–1346. PMLR, 2023. 13 PREPRINT Appendix A Additional Results on Synthetic Dataset A.1 Experimental Details Experiments on a synthetic dataset were conducted by simulating a t...

    work page 2023