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Multivariate Ordinal Patterns for Symmetry Approximation in Dynamic Probabilistic Relational Models

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 13151)

Abstract

Exploiting symmetries is an important topic to obtain sparse (lifted) representations, reduce complexity and achieve good performance in dynamic probabilistic relational models (DPRMs). DPRMs factorise a full joint probability distribution by encoding multivariate time series through a set of conditionally dependent random variables. As obtaining exact symmetries throughout multivariate time series is often not realistic in real-world contexts and counteracts lifted representations, we propose to approximate the multivariate time series with a symbolisation scheme that encodes the overarching trend in up and down movements. In this work, we introduce MOP4SA, an approach for the approximation of symmetries based on multivariate ordinal pattern encodings and spectral clustering. Understanding symmetrical behaviour has several benefits that we evaluate in two use cases. We use MOP4SA (a) to detect structures in model symmetries over time, and (b) to avoid model splits and groundings in DPRMs.

Keywords

  • Symmetry
  • Multivariate time series
  • Multivariate ordinal pattern
  • Relational models
  • Lifting

N. Finke and M. Mohr—Contributed equally to this work.

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Notes

  1. 1.

    Pronounced deeper models.

  2. 2.

    https://www.dma.dk/SikkerhedTilSoes/Sejladsinformation/AIS/.

  3. 3.

    https://github.com/FinkeNils/Processed-AIS-Data-Baltic-Sea-2020-v2.

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Finke, N., Möller, R., Mohr, M. (2022). Multivariate Ordinal Patterns for Symmetry Approximation in Dynamic Probabilistic Relational Models. In: Long, G., Yu, X., Wang, S. (eds) AI 2021: Advances in Artificial Intelligence. AI 2022. Lecture Notes in Computer Science(), vol 13151. Springer, Cham. https://doi.org/10.1007/978-3-030-97546-3_44

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  • DOI: https://doi.org/10.1007/978-3-030-97546-3_44

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