Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems

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dc.contributor.authorDamiyev, Zhaksybek
dc.contributor.editorTakhanov, Rustem
dc.contributor.otherTourassis, Vassilios D.
dc.date.accessioned2019-08-29T04:41:48Z
dc.date.available2019-08-29T04:41:48Z
dc.date.issued2019-05-01
dc.descriptionSubmitted to the Department of Mathematics on May 1, 2019, in partial fulfillment of the requirements for the degree of Master of Applied Mathematicsen_US
dc.description.abstractIn this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (𝐴,𝐵,𝐶,𝐷), from system’s past behaviour. First, we reproduced experimentally the well-known result of Hardt et al. that the reconstruction can be made under some conditions, called Pac-Man conditions. Then we demonstrated experimentally that the system approaches the global minimum even if an input 𝑥 is a sequence of i.i.d. random variables with a nongaussian distribution. We also formulated hypotheses beyond Pac-Man conditions that Gradient Descent solves the problem if the operator norm (or alternatively, the spectral radius) of transition matrix 𝐴 is bounded by 1 and obtained the negative result, i.e. a counterexample to those conjectures.en_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4191
dc.language.isoenen_US
dc.publisherNazarbayev University School of Science and Technologyen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectResearch Subject Categories::MATHEMATICS::Applied mathematicsen_US
dc.subjectdiscrete dynamical systemen_US
dc.titleExperimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systemsen_US
dc.typeMaster's thesisen_US
workflow.import.sourcescience

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