# Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

arXiv: https://arxiv.org/abs/2606.18993 · HTML: https://mlsanity.com/paper/2606.18993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Invariant and Transportable Representations for Anti-Causal Domain Shifts](https://mlsanity.com/paper/2207.01603/) (2022)
- [Sequential Kernelized Independence Testing](https://mlsanity.com/paper/2212.07383/) (2022)
- [Dimension-agnostic inference using cross U-statistics](https://mlsanity.com/paper/2011.05068/) (2020)
- [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)
- [E-Valuating Classifier Two-Sample Tests](https://mlsanity.com/paper/2210.13027/) (2022)
- [Conditional independence testing under misspecified inductive biases](https://mlsanity.com/paper/2307.02520/) (2023)
- [Deep anytime-valid hypothesis testing](https://mlsanity.com/paper/2310.19384/) (2023)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Testing Conditional Mean Independence Using Generative Neural Networks](https://mlsanity.com/paper/2501.17345/) (2025)
- [Distribution-uniform anytime-valid sequential inference and the Robbins-Siegmund distributions](https://mlsanity.com/paper/2311.03343/) (2023)

## Abstract (arXiv)

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.