Statistical Verification of Linear Classifiers
This work provides a statistical verification method for linear classifiers, specifically applied to gene expression analysis in breast cancer, but it is incremental as it focuses on refining bounds for a known test.
The authors tackled the problem of verifying whether a linear classifier meaningfully distinguishes between two classes by proposing a homogeneity test related to linear separability, and they applied it to confirm the significance of IGFBP6 and ELOVL5 genes in detecting ER-positive breast cancer recurrence.
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.