Research map / Probabilistic and scientific modeling / Causal discovery
Differentiable and score-based DAG learning
Learn causal DAGs by continuous optimization, reinforcement learning, or noise-model assumptions.
52 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Causal discovery, keyword cluster “causal discovery · causal structure · graphs”
State History Tried Baselines Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
17 papers in 2023–24 and 20 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 7.3% to 6.0%.
Open questions the data points to
- Papers report GraN-DAG on Sachs (SHD) anywhere from 13 to 16: comparisons against it depend on whose number you take.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Separators and Adjustment Sets in Markov Equivalent DAGs (AAAI 2016 · 16 citations)
- 2017 · Permutation-based Causal Inference Algorithms with Interventions (NeurIPS 2017 · 56 citations)
- 2018 · Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions (ICML 2018 · 36 citations)
- 2019 · Counting and Sampling from Markov Equivalent DAGs Using Clique Trees (AAAI 2019 · 15 citations)
- 2020 · Gradient-Based Neural DAG Learning (ICLR 2020 · 15 citations)
- 2021 · Integer Programming for Causal Structure Learning in the Presence of Latent Variables (ICML 2021 · 5 citations)
- 2022 · Granger causal inference on DAGs identifies genomic loci regulating transcription (ICLR 2022 · 5 citations)
- 2023 · Reinforcement Causal Structure Learning on Order Graph (AAAI 2023 · 15 citations)
- 2024 · Stable Differentiable Causal Discovery (ICML 2024 · 4 citations)
- 2025 · Boosting Causal Structure Learning: An Asymmetric Exponential Modulation Gaussian-Based Adaptive Sample Reweighting Framework (AAAI 2025 · 0 citations)
- 2026 · PACER: Acyclic Causal Discovery from Large-scale Interventional Data (ICML 2026 · 0 citations)
Earliest papers here
- Separators and Adjustment Sets in Markov Equivalent DAGs (AAAI 2016 · 16 citations)
- Permutation-based Causal Inference Algorithms with Interventions (NeurIPS 2017 · 56 citations)
- Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions (ICML 2018 · 36 citations)
What has been tried
31 papers here report 278 measured changes (a component added, removed or swapped, compared with a baseline): helped 60%, no clear effect 13%, hurt 20%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Remove stage 1 edge preselection | Causal discovery simulations · convergence speed | Hurt | Stable Differentiable Causal Discovery (ICML 2024 · 4 citations) | |
| Use MCP or SCAD instead of quasi-MCP | Gaussian DAG models · Recovery of minimal equivalence class | No clear effect | Markov Equivalence and Consistency in Differentiable Structure Learning (NeurIPS 2024 · 1 citation) | |
| Use binary-masked path loss instead of intuitive relaxed path loss | Synthetic datasets · F1 | Helped | Differentiable Structure Learning with Ancestral Constraints (ICML 2025) | |
| Use a soft mask instead of a binary hard mask | K562 CAGE · MSE | 0.1863 -> 0.1856 | Helped | Learning to Discover Regulatory Elements for Gene Expression Prediction (ICLR 2025) |
Baseline numbers that disagree
The same baseline on the same benchmark and metric, reported more than 5% apart by different papers here. Training budgets, data splits and reimplementations differ, so state which number you compare with.
What reviewers will expect
Datasets and baselines named in the 13 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- Sachs flow cytometry · 2 of 13 papers
Baselines
- GOLEM · 3 of 13 papers
- NOTEARS · 2 of 13 papers
- DAGMA · 2 of 13 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 37 papers; from OpenAlex and the papers' affiliations).
- IBM · 3 papers
- Lehigh University · 2 papers
- Rensselaer Polytechnic Institute · 2 papers
- University of Science and Technology of China · 2 papers
- Microsoft · 2 papers
- Carnegie Mellon University · 2 papers
- University of Oxford · 2 papers
- KTH Royal Institute of Technology · 2 papers
- Nanjing University · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Constraint-based structure learning with latents (90 papers)
- Identifiability with hidden confounders (85 papers)
- Interventional causal discovery (68 papers)
- Causal discovery from time series (51 papers)
Elsewhere in the topic
- Causal representation identifiability (122 papers)
- Latent-variable causal estimation (117 papers)
- Causal effect identification (107 papers)
- Counterfactual identification and bounds (92 papers)
- Causal approaches to fairness (46 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).