幂变换再探：数值稳定与联邦学习

Power Transform Revisited: Numerically Stable, and Federated

October 6, 2025

作者: Xuefeng Xu, Graham Cormode

cs.AI

摘要

幂变换是一种常用的参数化技术，旨在使数据更接近高斯分布，在统计分析和机器学习中作为预处理步骤被广泛应用。然而，我们发现幂变换的直接实现存在严重的数值不稳定性，可能导致错误结果甚至系统崩溃。本文深入分析了这些不稳定性的根源，并提出了有效的解决方案。此外，我们将幂变换扩展到联邦学习场景，解决了该环境下出现的数值和分布挑战。在真实数据集上的实验表明，我们的方法既有效又稳健，与现有方法相比显著提升了稳定性。

English

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.