发表机构
University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于能量距离的置换检验PTED，一种多维双样本检验方法，适用于高维、不平衡样本及任意距离定义的数据，且线性扩展，并在敏感性测试中表现优于其他方法。
AI 中文摘要
双样本检验在推断和生成建模中应用广泛，然而由于缺乏一种可在多维空间中操作的易用检验方法，用户常常退而求助于启发式方法和视觉检查。我提出了基于能量距离的置换检验（Permutation Test using the Energy Distance，PTED），这是Székely和Rizzo [2004]所描述的一种强大双样本检验的Python实现。检验统计量为能量距离，这是一种概率分布上的度量，其自然样本估计量由成对距离构建。在能量距离上运行置换检验，可产生精确的双样本检验。由于该统计量仅通过成对距离依赖于数据，因此该检验适用于高维数据、学习到的特征表示、大样本或小样本或不平衡样本量，以及任何可定义距离的数据类型。对该公式的近似使得PTED能够在线性时间内随维度和样本数量扩展，同时保留大部分判别能力。我重点展示了PTED上的一系列具有启发性的敏感性测试，并与其他多维双样本检验进行比较。PTED是唯一对所有测试都敏感的方法，而传统的最大均值差异（Maximum Mean Discrepancy）除了一项过拟合测试外，在其他所有测试中表现相同。
英文摘要
Two-sample tests are widely applicable in inference and generative modelling, yet users frequently fall back on heuristics and visual inspection due to lack of an accessible test that operates in multiple dimensions. I present Permutation Test using the Energy Distance (PTED), a Python implementation of a powerful two-sample test described in Székely and Rizzo [2004]. The test statistic is the energy distance, a metric on probability distributions that admits a natural sample estimator built from pairwise distances. A permutation test is run on energy distances to produce an exact two-sample test. Because the statistic depends on the data only through pairwise distances, the test applies in high dimensions, on learned feature representations, at large or small or imbalanced sample sizes, and to any data type on which a distance can be defined. An approximation to the formula allows PTED to scale linearly with both number of dimensions and samples while retaining most discriminative power. I highlight a number of instructive sensitivity tests on PTED alongside other multi-dimensional two-sample tests for comparison. PTED is the only method that is sensitive to all tests, though conventional Maximum Mean Discrepancy is identical for all but an over-fitting test.
Comments23 pages, 14 figures, 1 table, Proceedings of the 2026 Joint Statistical Meetings (JSM)
