<div class="csl-bib-body">
<div class="csl-entry">Radojičić, U., Mayrhofer, M., & Filzmoser, P. (2024, October 25). <i>Explainable Outlier Detection for Multivariate Functional Data</i> [Presentation]. Turku Applied Mathematics and Statistics Seminar, Finland. http://hdl.handle.net/20.500.12708/210711</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/210711
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dc.description.abstract
This work addresses the challenges of robust covariance estimation and interpretable outlier
detection for multivariate functional data with separable covariance structures. Our goal is to
develop a method that simultaneously improves robustness and interpretability in this context.
We establish a connection between stochastic processes with separable covariance structures
and the corresponding matrix-variate distribution of their basis representations. Leveraging this
connection, we employ the Matrix Minimum Covariance Determinant (MMCD) approach introduced by [Mayrhofer et al., 2024], in conjunction with a multivariate functional Mahalanobis
(semi-)distance introduced in [Galeano et al., 2015], to robustly estimate both mean and covariance functions for multivariate functional data. For interpretable outlier detection, we propose
a methodology that applies Shapley values from game theory to decompose overall outlyingness into component-specific contributions. Importantly, we reduce the otherwise exponential
computational complexity (relative to the number of components) to linear complexity, while
retaining the key properties of the Shapley value. This integrated framework—combining robust
Mahalanobis distances, MMCD estimators, and Shapley value-based outlyingness decomposition
provides a robust and interpretable approach for analyzing multivariate functional data with
separable covariance structures. The effectiveness of this approach is demonstrated through
both theoretical analysis and practical applications, including simulations and real-world case
studies.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
FDA
en
dc.title
Explainable Outlier Detection for Multivariate Functional Data
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
I 5799-N
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dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.project.title
Generalisierte relative Daten und Robustheit in Bayes Räumen
