mlsanityData to 7 Oct 2026

NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning

arXiv 2301.01849 ↗First posted 4 Jan 2023cs.LG stat.ME stat.MLcited by 20

Not on the map. Why?

Abstract (arXiv)

Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the underlying causal graph is acyclic. While this is a convenient framework for developing theoretical developments about causal reasoning and inference, the underlying modeling assumption is likely to be violated in real systems, because feedback loops are common (e.g., in biological systems). Although a few methods search for cyclic causal models, they usually rely on some form of linearity, which is also limiting, or lack a clear underlying probabilistic model. In this work, we propose a novel framework for learning nonlinear cyclic causal graphical models from interventional data, called NODAGS-Flow. We perform inference via direct likelihood optimization, employing techniques from residual normalizing flows for likelihood estimation. Through synthetic experiments and an application to single-cell high-content perturbation screening data, we show significant performance improvements with our approach compared to state-of-the-art methods with respect to structure recovery and predictive performance.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 24 of its 54 references that are in the map. First posted on arXiv 4 Jan 2023.

Builds on

24 of 54 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,708
  4. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  7. 2018Invertible Residual Networkscited by 364
  8. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  9. 2019Residual Flows for Invertible Generative Modelingcited by 256
  10. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  11. 2019Learning Sparse Nonparametric DAGscited by 207
  12. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
12 more
  1. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  2. 2020Causal Autoregressive Flowscited by 97
  3. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  4. 2017Permutation-based Causal Inference Algorithms with Interventionscited by 78
  5. 2014Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Setscited by 48
  6. 2018Structural Agnostic Modeling: Adversarial Learning of Causal Graphscited by 48
  7. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  8. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  9. 2013A Discovery Algorithm for Directed Cyclic Graphscited by 33
  10. 2019The Case for Evaluating Causal Models Using Interventional Measures and Empirical Datacited by 30
  11. 2013Cyclic Causal Discovery from Continuous Equilibrium Datacited by 21
  12. 2020Structure Learning for Cyclic Linear Causal Modelscited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 6; 2025: 3; 2026: 8.

20 papers.

Sort:

By area:

  1. 2023GFlowNets for AI-Driven Scientific Discoverycited by 63
  2. 2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
  3. 2023Causal Modeling with Stationary Diffusionscited by 19
  4. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  5. 2024Recursive Causal Discoverycited by 12
  6. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  7. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4
  8. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  9. 2026Efficient Learning of Stationary Diffusions with Stein-type Discrepanciescited by 2
  10. 2024Learning Cyclic Causal Models from Incomplete Datacited by 1
  11. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  12. 2025Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networkscited by 1
8 more
  1. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 1
  2. 2026Consistency evaluation of benchmarks used for causal discoverycited by 1
  3. 2026Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventionscited by 0
  4. 2026RECLAIM: Cyclic Causal Discovery Amid Measurement Noisecited by 0
  5. 2026SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targetscited by 0
  6. 2026SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discoverycited by 0
  7. 2026CausalArena: Benchmarking Causal Discovery in the Foundation Model Eracited by 0
  8. 2026One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady Statecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning
  2. 2026Latent Confounded Causal Discovery via Lie Bracket Geometry
  3. 2023Causal normalizing flows: from theory to practice
  4. 2026Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives
  5. 2026Causal Reasoning with Bipartite Graphical Causal Models
  6. 2026Symmetries and Causality: Causal Effect Identification Beyond IID Data
  7. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference
  8. 2025dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Data