Predicting the Critical Number of Layers for Hierarchical Support Vector Regression
1
AIMdyn Inc., Santa Barbara, CA 93106, USA
2
Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
3
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Entropy 2021, 23(1), 37; https://doi.org/10.3390/e23010037
Received: 1 December 2020
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Revised: 21 December 2020
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Accepted: 22 December 2020
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Published: 29 December 2020
(This article belongs to the Special Issue Human-Centric AI: The Symbiosis of Human and Artificial Intelligence)
Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues. In the original formulation of HSVR, there were no rules for choosing the depth of the model. In this paper, we observe in a number of models a phase transition in the training error—the error remains relatively constant as layers are added, until a critical scale is passed, at which point the training error drops close to zero and remains nearly constant for added layers. We introduce a method to predict this critical scale a priori with the prediction based on the support of either a Fourier transform of the data or the Dynamic Mode Decomposition (DMD) spectrum. This allows us to determine the required number of layers prior to training any models.
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Keywords:
support vector regression; fourier transform; dynamic mode decomposition; koopman operator
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MDPI and ACS Style
Mohr, R.; Fonoberova, M.; Drmač, Z.; Manojlović, I.; Mezić, I. Predicting the Critical Number of Layers for Hierarchical Support Vector Regression. Entropy 2021, 23, 37. https://doi.org/10.3390/e23010037
AMA Style
Mohr R, Fonoberova M, Drmač Z, Manojlović I, Mezić I. Predicting the Critical Number of Layers for Hierarchical Support Vector Regression. Entropy. 2021; 23(1):37. https://doi.org/10.3390/e23010037
Chicago/Turabian StyleMohr, Ryan, Maria Fonoberova, Zlatko Drmač, Iva Manojlović, and Igor Mezić. 2021. "Predicting the Critical Number of Layers for Hierarchical Support Vector Regression" Entropy 23, no. 1: 37. https://doi.org/10.3390/e23010037
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