# Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models

arXiv: https://arxiv.org/abs/2405.14496 · HTML: https://mlsanity.com/paper/2405.14496/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 19 of 19)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling](https://mlsanity.com/paper/2310.18123/) (2023)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs](https://mlsanity.com/paper/2310.17816/) (2023)
- [Learning directed acyclic graphs based on sparsest permutations](https://mlsanity.com/paper/1307.0366/) (2013)
- [Greedy Approximation Algorithms for Active Sequential Hypothesis Testing](https://mlsanity.com/paper/2103.04250/) (2021)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)

## Built on by (most cited first, 5 of 5)

- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discovery](https://mlsanity.com/paper/2410.11759/) (2024)
- [When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery](https://mlsanity.com/paper/2506.23374/) (2025)
- [Stable Causal Discovery via Directed Acyclic Graph Aggregation](https://mlsanity.com/paper/2605.18633/) (2026)
- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)

## Abstract (arXiv)

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose strong parametric assumptions. To address these challenges, we propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We first present a topological sorting algorithm that leverages ancestral relationships in linear structural causal models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods. We demonstrate that this approach generalizes to nonlinear settings with arbitrary noise. We then introduce a nonparametric constraint-based algorithm that prunes spurious edges by searching for local conditioning sets, achieving greater accuracy than current methods. We provide theoretical guarantees for correctness and worst-case polynomial time complexities, with empirical validation on synthetic data.