arXiv:2605.22549v1 Announce Type: cross Abstract: The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$\chi^2$ null limits force a permutation calibration that multiplies the per-test cost by the number of permutations, in practice two orders of magnitude. Adapting the recent martingale MMD construction for two-sample testing to the (joint) independence problem, we introduce two studentised statistics whose null distributions are standard normal regardless of the data law, so that a
The continuous evolution of machine learning algorithms necessitates more efficient and accurate statistical independence tests to handle increasingly complex data structures.
This development offers a significant improvement in the statistical rigor and computational efficiency of independence testing, which is foundational for advanced AI model development and scientific research.
Machine learning practitioners and researchers can now employ a more statistically robust and computationally less demanding method for assessing independence between variables, reducing reliance on costly permutation calibrations.
- · AI/ML researchers
- · Data scientists
- · Cloud computing providers
- · SaaS companies leveraging advanced AI
- · Legacy statistical methods
- · Research groups reliant on less efficient computational techniques
Researchers can develop and validate more complex AI models faster and with greater confidence due to improved independence testing.
The reduced computational overhead may lead to more widespread application of these sophisticated statistical tests in various fields beyond core AI research.
More efficient model development could accelerate the deployment of agentic AI systems, as validating the independence of model components becomes less resource-intensive.
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