On Exact Distribution for Multivariate Weighted Distributions and Classification

• Published in: Methodology and computing in applied probability Vol. 25; no. 1; p. 41
• Main Author: Lamboni, Matieyendou
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2023; Springer Nature B.V
• Subjects: Behavior; Business and Management; Clustering; Distribution functions; Economics; Electrical Engineering; Life Sciences; Machine learning; Mathematics and Statistics; Multivariate analysis; Probability theory; Regression analysis; Sensitivity analysis; Statistics; Weighting functions; Dependency models; Copula; Multivariate weighted distributions; 62E10; 49Q12; Clustering; 65C50; Discrete variables; 60E05
• DOI: 10.1007/s11009-023-09993-2
• ISSN: 1387-5841

We are interested in analyzing specific model behaviors such as the model output(s) values within a given cluster using the probability theory. By showing the relevance of the multivariate weighted distribution theory to characterize some behaviors of interest thanks to the weight functions, we derive the distribution function of the model inputs that complies with a specific model behavior (called target inputs distribution). The target inputs lead to the target output(s) using the model, including clustering outcomes of rule-based ensembles, random forest, kernel-based learning and fuzzy clustering. Two expressions of that distribution are provided, including the copula. Conditional moments of the target output(s) and dependency models of the target inputs are also derived for the purpose of uncertainty quantification and sensitivity analysis. For computing such quantities of interest, consistent estimators and detailed illustrations of our approach are provided, including a real case study.