Alexander Shklyaev | Searcharxiv

arXiv2026

Survival Probability of Markov Linear Reccurence Sequence in a Random Environment: Subcritical Case

The Markov linear recurrence sequence in a random environment (MRSRE) is a particular case of Markov chain on non-negative integers. It is a natural generalization of several models with branching. We consider MRSRE with absorption at zero and study the survival time. We introduce a classification of subcritical MRSRE corresponding to that of branching process in a random environment. We show that general R-positivity theory can be applied to this model in a strongly subcritical case and prove the analogues of the Kolmogorov theorem and the Yaglom theorem. In other words, we describe the asymptotic behavior of the survival probability over a long time and the conditional distribution of the sequence, conditioned on the survival event. The results are applied to particular branching models.

math.PR↗

arXiv2025

Statistical Verification of Linear Classifiers

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.

stat.ML↗