# A Kernel Independence Test for Random Processes

arXiv: https://arxiv.org/abs/1402.4501 · HTML: https://mlsanity.com/paper/1402.4501/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2014.

## Built on by (most cited first, 18 of 18)

- [On Empirical Risk Minimization with Dependent and Heavy-Tailed Data](https://mlsanity.com/paper/2109.02224/) (2021)
- [Sequential Kernelized Independence Testing](https://mlsanity.com/paper/2212.07383/) (2022)
- [Learning Causal Graphs via Monotone Triangular Transport Maps](https://mlsanity.com/paper/2305.18210/) (2023)
- [Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series](https://mlsanity.com/paper/2305.08529/) (2023)
- [Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions](https://mlsanity.com/paper/2306.00904/) (2023)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Estimating R'enyi's α-Cross-Entropies in a Matrix-Based Way](https://mlsanity.com/paper/2109.11737/) (2021)
- [A Multiple kernel testing procedure for non-proportional hazards in factorial designs](https://mlsanity.com/paper/2206.07239/) (2022)
- [MPruner: Optimizing Neural Network Size with CKA-Based Mutual Information Pruning](https://mlsanity.com/paper/2408.13482/) (2024)
- [Permutation-Free High-Order Interaction Tests](https://mlsanity.com/paper/2506.05963/) (2025)
- [Survival Analysis of the Compressor Station Based on Hawkes Process with Weibull Base Intensity](https://mlsanity.com/paper/2112.13581/) (2021)
- [Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'](https://mlsanity.com/paper/2206.11142/) (2022)
- [Pitfalls of Climate Network Construction: A Statistical Perspective](https://mlsanity.com/paper/2211.02888/) (2022)
- [Multimodal Multi-User Surface Recognition with the Kernel Two-Sample Test](https://mlsanity.com/paper/2303.04930/) (2023)
- [Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes](https://mlsanity.com/paper/2305.18412/) (2023)
- [Robust Independence Tests with Finite Sample Guarantees for Synchronous Stochastic Linear Systems](https://mlsanity.com/paper/2308.02054/) (2023)
- [Causal Inference from Slowly Varying Nonstationary Processes](https://mlsanity.com/paper/2405.06902/) (2024)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)

## Abstract (arXiv)

A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world Forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives. The code is available online: https://github.com/kacperChwialkowski/HSIC .