# Non-Parametric Inference of Relational Dependence

arXiv: https://arxiv.org/abs/2207.00163 · HTML: https://mlsanity.com/paper/2207.00163/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Towards Robust Relational Causal Discovery](https://mlsanity.com/paper/1912.02390/) (2019)
- [Sobolev Independence Criterion](https://mlsanity.com/paper/1910.14212/) (2019)
- [An Experimental Study of Structural Diversity in Social Networks](https://mlsanity.com/paper/1909.03543/) (2019)

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

- [Relational Causal Discovery with Latent Confounders](https://mlsanity.com/paper/2507.01700/) (2025)

## Abstract (arXiv)

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is violated in many real-world datasets and applications centered on relational systems. This work examines the problem of estimating independence in data drawn from relational systems by defining sufficient representations for the sets of observations influencing individual instances. Specifically, we define marginal and conditional independence tests for relational data by considering the kernel mean embedding as a flexible aggregation function for relational variables. We propose a consistent, non-parametric, scalable kernel test to operationalize the relational independence test for non-i.i.d. observational data under a set of structural assumptions. We empirically evaluate our proposed method on a variety of synthetic and semi-synthetic networks and demonstrate its effectiveness compared to state-of-the-art kernel-based independence tests.