# Meta-Dependence in Conditional Independence Testing

arXiv: https://arxiv.org/abs/2504.12594 · HTML: https://mlsanity.com/paper/2504.12594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Separation-based distance measures for causal graphs](https://mlsanity.com/paper/2402.04952/) (2024)
- [Causal Information Splitting: Engineering Proxy Features for Robustness to Distribution Shifts](https://mlsanity.com/paper/2305.05832/) (2023)
- [Bayesian test of significance for conditional independence: The multinomial model](https://mlsanity.com/paper/1306.3627/) (2013)

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

- [Data Augmentation via Causal-Residual Bootstrapping](https://mlsanity.com/paper/2603.15335/) (2026)

## Abstract (arXiv)

Conditional independence testing is a critical component of feature screening, invariant statistical models, and causal discovery. Many of these algorithms rely on the sequential application of conditional independence tests, and their stability hinges on how their outcomes interact. We study this ``meta-dependence'' between conditional independence properties using the following geometric intuition: satisfying each conditional independence property constrains the space of possible joint distributions to a manifold. The ``meta-dependence'' of multiple conditional independences in a probability distribution is informed by its position relative to these manifolds. We provide a simple-to-compute measure of this meta-dependence using moment projections, with a closed-form expression for multivariate Gaussian distributions, and consolidate our findings empirically using both synthetic and real-world data. Our measure of meta-dependence does not rely on graphical properties of the distribution and can be computed directly from summary statistics such as a covariance matrix, allowing for various applications. We demonstrate one use case of meta-dependence, using a simple redundancy metric to tune significance thresholds and improve causal discovery.