Statistical Verification of Linear Classifiers

Anton Zhiyanov; Alexander Shklyaev; Alexey Galatenko; Vladimir Galatenko; Alexander Tonevitsky

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arXiv · 2501.14430

Statistical Verification of Linear Classifiers

Anton Zhiyanov·Alexander Shklyaev·Alexey Galatenko·Vladimir Galatenko·Alexander Tonevitsky

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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 whether a linear classifier is merely ``random'' or effectively captures differences between two classes. We focus on establishing upper bounds for the test's \emph{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 significance of IGFBP6 and ELOVL5 genes in this process.

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Anton Zhiyanov, Alexander Shklyaev, Alexey Galatenko, Vladimir Galatenko, Alexander Tonevitsky. 2025-01-24. Statistical Verification of Linear Classifiers. https://arxiv.org/abs/2501.14430

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