# Large-Scale Kernel Methods for Independence Testing

arXiv: https://arxiv.org/abs/1606.07892 · HTML: https://mlsanity.com/paper/1606.07892/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2016.

## Built on by (most cited first, 30 of 32)

- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Hybrid Random Features](https://mlsanity.com/paper/2110.04367/) (2021)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Measuring Dependence with Matrix-based Entropy Functional](https://mlsanity.com/paper/2101.10160/) (2021)
- [Sample Complexity of Probability Divergences under Group Symmetry](https://mlsanity.com/paper/2302.01915/) (2023)
- [A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSD](https://mlsanity.com/paper/2503.04820/) (2025)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [A Permutation-Free Kernel Independence Test](https://mlsanity.com/paper/2212.09108/) (2022)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [Localized Contrastive Learning on Graphs](https://mlsanity.com/paper/2212.04604/) (2022)
- [Entropy Regularized Optimal Transport Independence Criterion](https://mlsanity.com/paper/2112.15265/) (2021)
- [A Scalable Nystrom-Based Kernel Two-Sample Test with Permutations](https://mlsanity.com/paper/2502.13570/) (2025)
- [Nystr"om M-Hilbert-Schmidt Independence Criterion](https://mlsanity.com/paper/2302.09930/) (2023)
- [Causal Representation Learning in Temporal Data via Single-Parent Decoding](https://mlsanity.com/paper/2410.07013/) (2024)
- [A Unified View of Optimal Kernel Hypothesis Testing](https://mlsanity.com/paper/2503.07084/) (2025)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment](https://mlsanity.com/paper/2111.13226/) (2021)
- [A survey of some recent developments in measures of association](https://mlsanity.com/paper/2211.04702/) (2022)
- [Wind power predictions from nowcasts to 4-hour forecasts: a learning approach with variable selection](https://mlsanity.com/paper/2204.09362/) (2022)
- [Private independence testing across two parties](https://mlsanity.com/paper/2207.03652/) (2022)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [Testing using Privileged Information by Adapting Features with Statistical Dependence](https://mlsanity.com/paper/2111.02865/) (2021)
- [Non-Parametric Inference of Relational Dependence](https://mlsanity.com/paper/2207.00163/) (2022)
- [Bipartite Graph Variational Auto-Encoder with Fair Latent Representation to Account for Sampling Bias in Ecological Networks](https://mlsanity.com/paper/2403.02011/) (2024)
- [Fast Causal Discovery by Approximate Kernel-based Generalized Score Functions with Linear Computational Complexity](https://mlsanity.com/paper/2412.17717/) (2024)
- [Permutation-Free High-Order Interaction Tests](https://mlsanity.com/paper/2506.05963/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Bayesian Kernelised Test of (In)dependence with Mixed-type Variables](https://mlsanity.com/paper/2105.04001/) (2021)
- [Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'](https://mlsanity.com/paper/2206.11142/) (2022)
- [Learning nonparametric DAGs with incremental information via high-order HSIC](https://mlsanity.com/paper/2308.05969/) (2023)

## Abstract (arXiv)

Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including nonlinear associations and multivariate interactions. However, these approaches come with an at least quadratic computational cost in the number of observations, which can be prohibitive in many applications. Arguably, it is exactly in such large-scale datasets that capturing any type of dependence is of interest, so striking a favourable tradeoff between computational efficiency and test performance for kernel independence tests would have a direct impact on their applicability in practice. In this contribution, we provide an extensive study of the use of large-scale kernel approximations in the context of independence testing, contrasting block-based, Nystrom and random Fourier feature approaches. Through a variety of synthetic data experiments, it is demonstrated that our novel large scale methods give comparable performance with existing methods whilst using significantly less computation time and memory.