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Coherent Set Identification Via Direct Low Rank Maximum Likelihood Estimation

Titelangaben

Polzin, Robert M. ; Klebanov, Ilja ; Nüsken, Nikolas ; Koltai, Peter:
Coherent Set Identification Via Direct Low Rank Maximum Likelihood Estimation.
In: Journal of Nonlinear Science. Bd. 35 (2025) . - 2.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-024-10091-x

Dies ist die aktuelle Version des Eintrags.

Abstract

We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the action of a stochastic transition matrix in a way maximally distinguishable from other groups. The second one is a low rank factorization approach for stochastic matrices, called direct Bayesian model reduction (DBMR), which estimates the low rank factors directly from observed data. We show that DBMR results in a low rank model that is a projection of the full model, and exploit this insight to infer bounds on a quantitative measure of coherence within the reduced model. Both approaches can be formulated as optimization problems, and we also prove a bound between their respective objectives. On a broader scope, this work relates the two classical loss functions of nonnegative matrix factorization, namely the Frobenius norm and the generalized Kullback–Leibler divergence, and suggests new links between likelihood-based and projection-based estimation of probabilistic models.

Weitere Angaben

Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Dynamical Systems and Data > Lehrstuhl Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Dynamical Systems and Data
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 04 Nov 2024 08:22
Letzte Änderung: 04 Nov 2024 08:22
URI: https://eref.uni-bayreuth.de/id/eprint/90943

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