Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of misclassifying one specific class than the other. Neyman-Pearson (NP) paradigm was introduced in this context as a novel statistical framework for handling asymmetric...

This paper provides a rigorous analysis of the asymptotic behavior of the solution for the boundary-value problem u + u − 1 = 0, −1 < x < 1, u(−1) = u(1) = 0 as the parameter approaches zero.

In the Neyman-Pearson (NP) classification paradigm, the goal is to learn a classifier from labeled training data such that the probability of a false negative is minimized while the probability of a false positive is below a user-specified level α ∈ (0, 1). This work addresses the question of how to evaluate and compare classifiers in the NP setting. Simply reporting false positives and false n...

Abstract Multiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and Hessenberg, respectively, Gauss–Borel factorization of moment matrix is given. It shown a hidden freedom exhibited by system related multiple polynomials. Pearson equations discussed, Laguerre–Freud conside...