arXiv:2504.11299v2 Announce Type: replace-cross Abstract: We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multi-dimensional setting, and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the difference over orthogonal dominating rectangular ranges (d-sided rectangles in R^d), and is an integral probability metric. We also prove that the distance between a distribution and a sample from the distribution converges to 0 as the sample size grows, and bound this rate. Moreover, we show that one c
The continuous evolution of AI and machine learning fields necessitates more robust and efficient statistical tools for data comparison and analysis.
Improved multi-dimensional statistical distance metrics can lead to more accurate and reliable AI models, especially in complex data environments where traditional metrics fall short.
This research provides a more theoretically sound and practical method for comparing multi-dimensional probability distributions, which can enhance various machine learning applications.
- · AI researchers
- · Data scientists
- · Machine learning platform developers
- · Quant finance
- · Inefficient statistical methods
- · Models relying on simpler, less accurate multi-dimensional distance measures
More accurate and stable comparisons between complex datasets will become possible.
This could lead to advancements in areas like generative adversarial networks (GANs) and anomaly detection where distributional comparisons are critical.
Fundamental improvements in AI model reliability and interpretability could accelerate broader adoption in sensitive applications.
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Read at arXiv cs.LG