Research map / Probabilistic and scientific modeling / Causal discovery
Constraint-based structure learning with latents
Recover causal graphs under latent variables and mixed data using recursive, constraint-based algorithms.
90 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 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.
24 papers in 2023–24 and 40 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 10.3% to 12.0%.
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 · On Learning Causal Models from Relational Data (AAAI 2016 · 21 citations)
- 2017 · Discovering Causal Signals in Images (CVPR 2017 · 206 citations)
- 2018 · Bayesian Structure Learning by Recursive Bootstrap (NeurIPS 2018 · 11 citations)
- 2019 · Recursively Learning Causal Structures Using Regression-Based Conditional Independence Test (AAAI 2019 · 11 citations)
- 2020 · CASTLE: Regularization via Auxiliary Causal Graph Discovery (NeurIPS 2020 · 28 citations)
- 2021 · Improving Causal Discovery By Optimal Bayesian Network Learning (AAAI 2021 · 17 citations)
- 2022 · A Hybrid Causal Structure Learning Algorithm for Mixed-Type Data (AAAI 2022 · 14 citations)
- 2023 · Information-Theoretic Causal Discovery and Intervention Detection over Multiple Environments (AAAI 2023 · 5 citations)
- 2024 · Causal-learn: Causal Discovery in Python (NeurIPS 2024 · 26 citations)
- 2025 · DCILP: A Distributed Approach for Large-Scale Causal Structure Learning (AAAI 2025 · 5 citations)
- 2026 · Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families (ICML 2026 · 0 citations)
Earliest papers here
- On Learning Causal Models from Relational Data (AAAI 2016 · 21 citations)
- Discovering Causal Signals in Images (CVPR 2017 · 206 citations)
- Learning Causal Structures Using Regression Invariance (NeurIPS 2017 · 13 citations)
What has been tried
56 papers here report 466 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 9%, hurt 17%, 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 |
|---|---|---|---|---|
| Use topological information across nodes instead of same-node history only | Metropolitan Cellular Network Alarm Data · F1 | 0.38 -> 0.54 | Helped | TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences (AAAI 2024 · 6 citations) |
| use ground-truth Markov blankets instead of estimated blankets | SF3 (d=400, n/d=20) · SHD | 322 { ± 68.83} -> 208 { ± 24.43} | Helped | DCILP: A Distributed Approach for Large-Scale Causal Structure Learning (AAAI 2025 · 5 citations) |
| vary the embedding dimension | Rössler-Lorenz, C=1 · causal inference performance | Mixed | Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems (NeurIPS 2024 · 4 citations) | |
| Add the input-output Jacobian regularizer | VAR100 summary · AUPRC | 0.667 -> 0.950 | Helped | Jacobian Regularizer-based Neural Granger Causality (ICML 2024 · 2 citations) |
| add semi-supervised learning warmup rather than regular early stopping | CIFAR-10 IDN-50% · accuracy | 94.43 ± 0.07 -> 95.88 ± 0.08 | Helped | Learning the Latent Causal Structure for Modeling Label Noise (NeurIPS 2024 · 1 citation) |
| use two hidden layers of width 8 rather than one hidden layer of width 4 | 30 graphs · Expected SHD between CPDAGs | 3.63 -> 1.23 | Helped | Since Faithfulness Fails: The Performance Limits of Neural Causal Discovery (ICML 2025 · 0 citations) |
| Use positional embedding instead of LTE | ER synthetic graphs, D=30, 50, 100 · OD | 16.9 ± 6.12 -> 19.0 ± 6.91; 32.8 ± 6.55 -> 41.4 ± 11.33; 86.6 ± 12.99 -> 100.7 ± 15.62 | Hurt | Score-informed Neural Operator for Enhancing Ordering-based Causal Discovery (NeurIPS 2025 · 0 citations) |
| use ConservativeInsert instead of SafeInsert | ER graphs, observational data · structural error | Helped | Less Greedy Equivalence Search (NeurIPS 2025 · 0 citations) | |
| add Theorem 1 ordering instead of random topological ordering | Sachs · SHD | 17.0±3.50 -> 11.0±0.00 | Helped | Ordering-Based Causal Discovery for Linear and Nonlinear Relations (NeurIPS 2024 · 0 citations) |
| Remove the residual-independence term from order estimation | Synthetic weakly identifiable MLP problems · F1 Score | Hurt | Strong and Weak Identifiability of Optimization-based Causal Discovery in Non-linear Additive Noise Models (ICML 2025) |
What reviewers will expect
Datasets and baselines named in the 21 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- Tübingen cause-effect pairs · 2 of 21 papers
- Sachs · 2 of 21 papers
Baselines
- GES · 2 of 21 papers
- DAGMA · 2 of 21 papers
- CAM · 2 of 21 papers
- RESIT · 2 of 21 papers
- CaPS · 2 of 21 papers
- DiffAN · 2 of 21 papers
- SCORE · 2 of 21 papers
- RCD · 2 of 21 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 64 papers; from OpenAlex and the papers' affiliations).
- Mohamed bin Zayed University of Artificial Intelligence · 5 papers
- Guangdong University of Technology · 3 papers
- Monash University · 2 papers
- CISPA Helmholtz Center for Information Security · 2 papers
- Shantou University · 2 papers
- University of California, San Diego · 2 papers
- Beijing Technology and Business University · 2 papers
- Carnegie Mellon University · 2 papers
- East China Normal University · 2 papers
- University of Copenhagen · 2 papers
Use it
Download BibTeX of 37 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Identifiability with hidden confounders (85 papers)
- Interventional causal discovery (68 papers)
- Differentiable and score-based DAG learning (52 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).