Statistical Verification of Linear Classifiers
Anton Zhiyanov, Aleksandr V. Shklyaev, Alexei Vladimirovich Galatenko, Vladimir Vladimirovich Galatenko, A. G. Tonevitsky · Stat · 2025
ABSTRACT We propose a homogeneity test closely related to the concept of linear separability between two samples. Using the test, one can answer the question of whether a linear classifier is merely ‘random’ or effectively captures differences between two classes. We focus on establishing upper bounds for the test's p ‐value when applied to two‐dimensional samples. Specifically, for normally distributed samples, we experimentally demonstrate that the upper bound is highly accurate. Using this bound, we evaluate classifiers designed to detect ER‐positive breast cancer recurrence based on gene pair expression. Our findings confirm the significance of IGFBP6 and ELOVL5 genes in this process.