Fractionally Supervised Classification with Maxima Nominated Samples

Fractionally supervised classification (FSC) offers a flexible framework for combining labeled and unlabeled data in model-based classification, but existing formulations assume simple random sampling. In many applications, however, the retained observation is an extreme order statistic from a set rather than a randomly selected unit. This is particularly appealing when the target population is rare, since maxima nomination sampling (NS) can enrich the sample with the most informative observations, as in screening, environmental monitoring, repeated testing, and reliability studies. Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid. We develop FSC for nominated samples by introducing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting method yields a proper EM algorithm and a coherent weighted-likelihood FSC procedure for NS data. We present the methodology in general form, illustrate it for a rare-event contamination normal mixtures, and show through simulation that it substantially improves on the misspecified alternative by ignoring the extra rank information of such data. A real-data analysis demonstrates its practical value.

Elite-Driven Support Vector Machines for Classification

Support vector machines (SVMs) are a standard tool for binary classification, but their classical formulations are purely data-driven and offer no direct way to encode trusted benchmark models or structured preferences on selected subsets of the data. We propose Elite-Driven Support Vector Machines (EDSVM), a general framework that augments regularized empirical risk minimization by guiding the slack variables for a curated set of elite observations (typically the union of support vectors from one or more reference SVMs). EDSVM combines the usual slack loss with a deviation penalty that shrinks new slacks toward benchmark slack values, defining a localized, margin-aligned notion of proximity to reference models, unlike global function penalties in knowledge distillation or teacher-student methods, and without requiring privileged features as in SVM+/LUPI. Within this framework we develop two concrete models, C-EDSVM and LS-EDSVM, based respectively on hinge-type and squared-slack losses. For both variants we derive dual quadratic programs that can be implemented with modest modifications of standard SVM solvers, and we give simple sufficient conditions under which the induced margin losses are classification calibrated. Simulation studies and experiments on several UCI benchmarks show that EDSVMs closely track the behaviour induced by reference SVMs while achieving predictive performance that is competitive with, and sometimes better than, C-SVM, LINEX-SVM, and LS-SVM.