Classification with Bernstein copula as discrimination function

• Published in: Communications in statistics. Simulation and computation Vol. 54; no. 6; pp. 1852 - 1868
• Main Authors: Yamut, Tolga, Hudaverdi, Burcu
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03.06.2025
• Subjects: Bernstein copula; Breast cancer; Convex copula; Supervised learning
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2023.2299435

Bernstein copula models are handy tools for constructing higher-dimensional distribution structures. This study proposes a Bernstein copula model as a discrimination function to classify the given data through the machine learning process. The dependence structures among features are constructed by the Bernstein copulas, especially in the presence of tail dependence. The performance of the Bernstein copula models on the supervised learning algorithm is investigated via a comprehensive simulation study. A convex Bernstein (CB) framework is presented and some adjustments are made to the distribution calibration to obtain efficient and flexible solutions. For comparison, the parametric copula approach and Gaussian Naive Bayes are used. An empirical application based on the Coimbra breast cancer data is employed where the classification performance is additionally investigated with the CB density functions. A mixed Bernstein optimization method is also presented as a benchmark. It is observed that the combination of distributional information proves to be a useful tool in the discrimination process and the convex Bernstein density approach has the potential of improving the discrimination ability.