# Reframed GES with a Neural Conditional Dependence Measure

arXiv: https://arxiv.org/abs/2206.08531 · HTML: https://mlsanity.com/paper/2206.08531/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)

## Built on by (most cited first, 2 of 2)

- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)

## Abstract (arXiv)

In a nonparametric setting, the causal structure is often identifiable only up to Markov equivalence, and for the purpose of causal inference, it is useful to learn a graphical representation of the Markov equivalence class (MEC). In this paper, we revisit the Greedy Equivalence Search (GES) algorithm, which is widely cited as a score-based algorithm for learning the MEC of the underlying causal structure. We observe that in order to make the GES algorithm consistent in a nonparametric setting, it is not necessary to design a scoring metric that evaluates graphs. Instead, it suffices to plug in a consistent estimator of a measure of conditional dependence to guide the search. We therefore present a reframing of the GES algorithm, which is more flexible than the standard score-based version and readily lends itself to the nonparametric setting with a general measure of conditional dependence. In addition, we propose a neural conditional dependence (NCD) measure, which utilizes the expressive power of deep neural networks to characterize conditional independence in a nonparametric manner. We establish the optimality of the reframed GES algorithm under standard assumptions and the consistency of using our NCD estimator to decide conditional independence. Together these results justify the proposed approach. Experimental results demonstrate the effectiveness of our method in causal discovery, as well as the advantages of using our NCD measure over kernel-based measures.