# Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency

arXiv: https://arxiv.org/abs/2406.09177 · HTML: https://mlsanity.com/paper/2406.09177/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 67 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 30 of 36)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [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)
- [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)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [A polynomial-time algorithm for learning nonparametric causal graphs](https://mlsanity.com/paper/2006.11970/) (2020)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [Invariant Representation Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2011.12379/) (2020)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [Optimizing NOTEARS Objectives via Topological Swaps](https://mlsanity.com/paper/2305.17277/) (2023)

## Built on by (most cited first, 6 of 6)

- [Arrow: A Foundation Model for Causal Discovery](https://mlsanity.com/paper/2605.07204/) (2026)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Causal Intervention Sequence Analysis for Fault Tracking in Radio Access Networks](https://mlsanity.com/paper/2511.17505/) (2025)
- [CausalT5k: Diagnosing Refusal and Failure Modes in Trustworthy Causal Reasoning Across Causal Rungs](https://mlsanity.com/paper/2602.08939/) (2026)
- [Neural Autoregressive Flows for Markov Boundary Learning](https://mlsanity.com/paper/2603.20791/) (2026)
- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

To make accurate predictions, understand mechanisms, and design interventions in systems of many variables, we wish to learn causal graphs from large scale data. Unfortunately the space of all possible causal graphs is enormous so scalably and accurately searching for the best fit to the data is a challenge. In principle we could substantially decrease the search space, or learn the graph entirely, by testing the conditional independence of variables. However, deciding if two variables are adjacent in a causal graph may require an exponential number of tests. Here we build a scalable and flexible method to evaluate if two variables are adjacent in a causal graph, the Differentiable Adjacency Test (DAT). DAT replaces an exponential number of tests with a provably equivalent relaxed problem. It then solves this problem by training two neural networks. We build a graph learning method based on DAT, DAT-Graph, that can also learn from data with interventions. DAT-Graph can learn graphs of 1000 variables with state of the art accuracy. Using the graph learned by DAT-Graph, we also build models that make much more accurate predictions of the effects of interventions on large scale RNA sequencing data.