# Amortized Conditional Independence Testing

arXiv: https://arxiv.org/abs/2502.20925 · HTML: https://mlsanity.com/paper/2502.20925/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 28 Feb 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Self-Attention Between Datapoints: Going Beyond Individual Input-Output Pairs in Deep Learning](https://mlsanity.com/paper/2106.02584/) (2021)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Diffeomorphic Information Neural Estimation](https://mlsanity.com/paper/2211.10856/) (2022)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [Wasserstein Conditional Independence Testing](https://mlsanity.com/paper/2107.14184/) (2021)
- [MIND: Inductive Mutual Information Estimation, A Convex Maximum-Entropy Copula Approach](https://mlsanity.com/paper/2102.13182/) (2021)

## Built on by (most cited first, 1 of 1)

- [DCD-PFN: A Decoupling-Aware Foundation Model for Causal Discovery](https://mlsanity.com/paper/2606.21212/) (2026)

## Abstract (arXiv)

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific disciplines. Existing methods seek to design explicit test statistics that quantify the degree of conditional dependence, which is highly challenging yet cannot capture nor utilize prior knowledge in a data-driven manner. In this study, an entirely new approach is introduced, where we instead propose to amortize conditional independence testing and devise ACID - a novel transformer-based neural network architecture that learns to test for conditional independence. ACID can be trained on synthetic data in a supervised learning fashion, and the learned model can then be applied to any dataset of similar natures or adapted to new domains by fine-tuning with a negligible computational cost. Our extensive empirical evaluations on both synthetic and real data reveal that ACID consistently achieves state-of-the-art performance against existing baselines under multiple metrics, and is able to generalize robustly to unseen sample sizes, dimensionalities, as well as non-linearities with a remarkably low inference time.