# Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning

arXiv: https://arxiv.org/abs/2510.04970 · HTML: https://mlsanity.com/paper/2510.04970/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 58 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Selective Greedy Equivalence Search: Finding Optimal Bayesian Networks Using a Polynomial Number of Score Evaluations](https://mlsanity.com/paper/1506.02113/) (2015)
- [Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms](https://mlsanity.com/paper/2107.03863/) (2021)
- [Extremely Greedy Equivalence Search](https://mlsanity.com/paper/2502.19551/) (2025)
- [Causal discovery in a complex industrial system: A time series benchmark](https://mlsanity.com/paper/2310.18654/) (2023)
- [Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method](https://mlsanity.com/paper/2405.13100/) (2024)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [MIDAS - An Influence Diagram for Management of Mildew in Winter Wheat](https://mlsanity.com/paper/1302.3587/) (2013)

## Built on by (most cited first, 4 of 4)

- [I-FLOP: Fast Learning of Order and Parents from Interventional Data](https://mlsanity.com/paper/2608.28245/) (2026)
- [Learning Causal Structure of Time Series using Best Order Score Search](https://mlsanity.com/paper/2603.05370/) (2026)
- [A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs](https://mlsanity.com/paper/2605.06288/) (2026)
- [Score-Based Learning of Cluster DAGs from Interventions](https://mlsanity.com/paper/2610.11947/) (2026)

## Abstract (arXiv)

We present FLOP (Fast Learning of Order and Parents), a score-based causal discovery algorithm for linear models. It pairs fast parent selection with iterative Cholesky-based score updates, cutting run-times over prior algorithms. This makes it feasible to fully embrace discrete search, enabling iterated local search with principled order initialization to find graphs with scores at or close to the global optimum. The resulting structures are highly accurate across benchmarks, with near-perfect recovery in standard settings. This performance calls for revisiting discrete search over graphs as a reasonable approach to causal discovery.