Power Transform Revisited: Numerically Stable, and Federated
Authors: name: Xuefeng Xu; name: Graham Cormode
Published: 2025-10-06 16:32:22

Abstract: 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.