# Sequential Kernelized Independence Testing

arXiv: https://arxiv.org/abs/2212.07383 · HTML: https://mlsanity.com/paper/2212.07383/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 15 of 15)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015)
- [A Kernel Independence Test for Random Processes](https://mlsanity.com/paper/1402.4501/) (2014)
- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [Anytime Valid Tests of Conditional Independence Under Model-X](https://mlsanity.com/paper/2209.12637/) (2022)
- [A simpler condition for consistency of a kernel independence test](https://mlsanity.com/paper/1501.06103/) (2015)

## Built on by (most cited first, 16 of 16)

- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [Active, anytime-valid risk controlling prediction sets](https://mlsanity.com/paper/2406.10490/) (2024)
- [Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2410.22318/) (2024)
- [Deep anytime-valid hypothesis testing](https://mlsanity.com/paper/2310.19384/) (2023)
- [Optimistic Interior Point Methods for Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2502.07774/) (2025)
- [Combining Evidence Across Filtrations](https://mlsanity.com/paper/2402.09698/) (2024)
- [I Bet You Did Not Mean That: Testing Semantic Importance via Betting](https://mlsanity.com/paper/2405.19146/) (2024)
- [The Minimax Rate of HSIC Estimation for Translation-Invariant Kernels](https://mlsanity.com/paper/2403.07735/) (2024)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Sequential Kernelized Stein Discrepancy](https://mlsanity.com/paper/2409.17505/) (2024)
- [Multi-Armed Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2603.17925/) (2026)
- [A complete characterization of sequential testability and change detectability in i.i.d. models](https://mlsanity.com/paper/2609.05752/) (2026)
- [Sequential Kernel-based Conditional Independence Testing via Adaptive Betting](https://mlsanity.com/paper/2606.18993/) (2026)
- [The Price of Peeking: Anytime-Valid Leakage Detection on ML-KEM EM Traces](https://mlsanity.com/paper/2609.33597/) (2026)
- [Always-On Experimentation](https://mlsanity.com/paper/2609.38695/) (2026)
- [Learning to Detect Shifts in Unstructured Data Streams via Monitoring-by-Betting](https://mlsanity.com/paper/2610.17399/) (2026)

## Abstract (arXiv)

Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) stop earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. Classical batch tests are not tailored for streaming data: valid inference after data peeking requires correcting for multiple testing which results in low power. Following the principle of testing by betting, we design sequential kernelized independence tests that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g., the Hilbert-Schmidt independence criterion. Our test is also valid under non-i.i.d., time-varying settings. We demonstrate the power of our approaches on both simulated and real data.