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[2602.22334] A 1/R Law for Kurtosis Contrast in Balanced Mixtures
Summary
This paper presents a new redundancy law for kurtosis contrast in balanced mixtures, demonstrating how effective width impacts kurtosis estimation and contrast recovery in machine learning applications.
Why It Matters
Understanding kurtosis contrast is crucial for improving independent component analysis (ICA) in machine learning. This research provides insights into the limitations of current methods and proposes solutions that could enhance data analysis techniques in various applications.
Key Takeaways
- Introduces a redundancy law for kurtosis contrast in balanced mixtures.
- Establishes that excess kurtosis is inversely related to effective width.
- Demonstrates the necessity of purification for restoring contrast independence.
- Validates theoretical predictions through synthetic experiments.
- Highlights the limitations of current kurtosis estimation methods.
Computer Science > Machine Learning arXiv:2602.22334 (cs) [Submitted on 25 Feb 2026] Title:A 1/R Law for Kurtosis Contrast in Balanced Mixtures Authors:Yuda Bi, Wenjun Xiao, Linhao Bai, Vince D Calhoun View a PDF of the paper titled A 1/R Law for Kurtosis Contrast in Balanced Mixtures, by Yuda Bi and 3 other authors View PDF HTML (experimental) Abstract:Kurtosis-based Independent Component Analysis (ICA) weakens in wide, balanced mixtures. We prove a sharp redundancy law: for a standardized projection with effective width $R_{\mathrm{eff}}$ (participation ratio), the population excess kurtosis obeys $|\kappa(y)|=O(\kappa_{\max}/R_{\mathrm{eff}})$, yielding the order-tight $O(c_b\kappa_{\max}/R)$ under balance (typically $c_b=O(\log R)$). As an impossibility screen, under standard finite-moment conditions for sample kurtosis estimation, surpassing the $O(1/\sqrt{T})$ estimation scale requires $R\lesssim \kappa_{\max}\sqrt{T}$. We also show that \emph{purification} -- selecting $m\!\ll\!R$ sign-consistent sources -- restores $R$-independent contrast $\Omega(1/m)$, with a simple data-driven heuristic. Synthetic experiments validate the predicted decay, the $\sqrt{T}$ crossover, and contrast recovery. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2602.22334 [cs.LG] (or arXiv:2602.22334v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2602.22334 Focus to learn more arXiv-issued DOI via DataCite (pend...
