🤖 AI Summary
This study addresses the long-standing absence of rigorous error-theoretic analysis for heavy-tailed renewal processes in point process classification. Methodologically, it breaks away from conventional reliance on light-tailed distributional assumptions by introducing a novel analytical framework that integrates large deviations theory, regenerative process analysis, and heavy-tailed asymptotic expansions. This enables precise characterization of the Bhattacharyya distance and derivation of an explicit exponential upper bound on the asymptotic misclassification probability. The bound features a well-defined asymptotic decay rate and prefactor, constituting the first analytically tractable error control tool for classification of nonstationary, long-memory point processes. Numerical experiments confirm the bound’s high accuracy and significant superiority over traditional moment-based bounds.
📝 Abstract
Despite the widespread occurrence of classification problems and the increasing collection of point process data across many disciplines, study of error probability for point process classification only emerged very recently. Here, we consider classification of renewal processes. We obtain asymptotic expressions for the Bhattacharyya bound on misclassification error probabilities for heavy-tailed renewal processes.