mlsanityData to 7 Oct 2026

NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge

arXiv 2109.04286 ↗First posted 9 Sep 2021cs.LG cs.AI stat.MLcited by 33

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Abstract (arXiv)

We describe NTS-NOTEARS, a score-based structure learning method for time-series data to learn dynamic Bayesian networks (DBNs) that captures nonlinear, lagged (inter-slice) and instantaneous (intra-slice) relations among variables. NTS-NOTEARS utilizes 1D convolutional neural networks (CNNs) to model the dependence of child variables on their parents; 1D CNN is a neural function approximation model well-suited for sequential data. DBN-CNN structure learning is formulated as a continuous optimization problem with an acyclicity constraint, following the NOTEARS DAG learning approach. We show how prior knowledge of dependencies (e.g., forbidden and required edges) can be included as additional optimization constraints. Empirical evaluation on simulated and benchmark data show that NTS-NOTEARS achieves state-of-the-art DAG structure quality compared to both parametric and nonparametric baseline methods, with improvement in the range of 10-20% on the F1-score. We also evaluate NTS-NOTEARS on complex real-world data acquired from professional ice hockey games that contain a mixture of continuous and discrete variables. The code is available online.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 20 of its 47 references that are in the map. First posted on arXiv 9 Sep 2021.

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20 of 47 references.

References · 20

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2017Detecting causal associations in large nonlinear time series datasetscited by 240
  3. 2019Gradient-Based Neural DAG Learningcited by 227
  4. 2019Learning Sparse Nonparametric DAGscited by 207
  5. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  6. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  7. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  8. 2020Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasetscited by 136
  9. 2020Causal Autoregressive Flowscited by 97
  10. 2020High-recall causal discovery for autocorrelated time series with latent confounderscited by 82
  11. 2017Conditional independence testing based on a nearest-neighbor estimator of conditional mutual informationcited by 70
  12. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
8 more
  1. 2019Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causalitycited by 55
  2. 2017Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulationscited by 51
  3. 2021Interpretable Models for Granger Causality Using Self-explaining Neural Networkscited by 44
  4. 2019End-to-End Environmental Sound Classification using a 1D Convolutional Neural Networkcited by 20
  5. 2017Network structure from rich but noisy datacited by 17
  6. 2020Cracking the Black Box: Distilling Deep Sports Analyticscited by 12
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Citing papers per year: 2022: 1; 2023: 3; 2024: 9; 2025: 10; 2026: 10.

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  1. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 35
  2. 2023Discovering Causal Relations and Equations from Datacited by 33
  3. 2024MECD: Unlocking Multi-Event Causal Discovery in Video Reasoningcited by 23
  4. 2025Causal-Copilot: An Autonomous Causal Analysis Agentcited by 14
  5. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  6. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  7. 2024Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discoverycited by 6
  8. 2025MECD+: Unlocking Event-Level Causal Graph Discovery for Video Reasoningcited by 5
  9. 2025Causal Climate Emulation with Bayesian Filteringcited by 5
  10. 2025Differentiable Constraint-Based Causal Discoverycited by 4
  11. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  12. 2024LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Datacited by 2
21 more
  1. 2025Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noisescited by 2
  2. 2025Robust Causal Discovery under Imperfect Structural Constraintscited by 2
  3. 2026Coarse-to-Fine Learning of Dynamic Causal Structurescited by 2
  4. 2026A Knowledge-Informed Pretrained Model for Causal Discoverycited by 2
  5. 2023A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representationscited by 1
  6. 2024Why Online Reinforcement Learning is Causalcited by 1
  7. 2024TS-CausalNN: Learning Temporal Causal Relations from Non-linear Non-stationary Time Series Datacited by 1
  8. 2024Fast Causal Discovery by Approximate Kernel-based Generalized Score Functions with Linear Computational Complexitycited by 1
  9. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  10. 2025Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphscited by 1
  11. 2024Causality-driven Sequence Segmentation for Enhancing Multiphase Industrial Process Data Analysis and Soft Sensingcited by 0
  12. 2025SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Inputcited by 0
  13. 2025Linear Causal Discovery with Interventional Constraintscited by 0
  14. 2026Transformer Is Inherently a Causal Learnercited by 0
  15. 2026SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphscited by 0
  16. 2026Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectivescited by 0
  17. 2026Integrating Causal DAGs in Deep RL: Activating Minimal Markovian States with Multi-Order Exposurecited by 0
  18. 2026TTCD:Transformer Integrated Temporal Causal Discovery from Non-Stationary Time Series Datacited by 0
  19. 2026Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretrainingcited by 0
  20. 2026ITSY: Causal Discovery From Irregular Time-Series Datacited by 0
  21. 2026LUCID: Learning Under Confounding for Inference and Discovery in Time Seriescited by 0