<div class="csl-bib-body">
<div class="csl-entry">Radojicic, U., Mayrhofer, M., & Filzmoser, P. (2024, December 17). <i>Expainable outlier detection for multivariate random processes with separable covariance structure</i> [Conference Presentation]. ICSDS2024, Nizza, France. http://hdl.handle.net/20.500.12708/210712</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/210712
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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. We develop a method that simultaneously improves robustness and interpretability in this context by establishing 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 recently developed matrix-variate counterpart of the Minimum Covariance Determinant estimator (MMCD) in conjunction with a truncated multivariate functional Mahalanobis semi-distance to robustly estimate mean and covariance for multivariate functional data. For interpretable outlier detection, we generalize multivariate outlier explanations based on Shapley values to decompose overall multivariate functional outlyingness into time-coordinate-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 examples.
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
FDA
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dc.subject
Separable covariance
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dc.subject
Random process
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dc.subject
Robustness
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dc.title
Expainable outlier detection for multivariate random processes with separable covariance structure
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
I 5799-N
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.project.title
Generalisierte relative Daten und Robustheit in Bayes Räumen
