Multivariate outlier explanations using Shapley values and Mahalanobis distances
Year: 2023
Type: article
Abstract: For the purpose of explaining multivariate outlyingness, it is shown that the squared Mahalanobis distance of an observation can be decomposed into outlyingness contributions originating from single variables. The decomposition is obtained using the Shapley value, a well-known concept from game theory that became popular in the context of Explainable AI. In addition to outlier explanation, this concept also relates to the recent formulation of cellwise outlyingness, where Shapley values can be employed to obtain variable contributions for outlying observations with respect to their “expected” position given the multivariate data structure. In combination with squared Mahalanobis distances, Shapley values can be calculated at a low numerical cost, making them an even more attractive tool for outlier interpretation. Simulations and real-world data examples demonstrate the usefulness of these concepts.
Source: Econometrics and Statistics
Authors: Marcus Mayrhofer, Peter Filzmoser
Institution: TU Wien
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,540
Funders: Bundesministerium für Klimaschutz, Umwelt, Energie, Mobilität, Innovation und Technologie, European Commission, Österreichische Forschungsförderungsgesellschaft, Electronic Components and Systems for European Leadership, Horizon 2020 Framework Programme, HORIZON EUROPE Framework Programme, Technische Universität Wien Bibliothek
OpenAlex ID: W4367315567