Anyszka, Wojciech (2024) Towards an Approximation Theory of Observable Operator Models. Bachelor's Thesis, Artificial Intelligence.
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Abstract
Observable operator models (OOMs) offer a powerful framework for modelling stochastic processes, surpassing the traditional hidden Markov models (HMMs) in generality and efficiency. However, using OOMs to model infinite-dimensional processes poses significant theoretical challenges. This thesis presents an exploration of a rigorous approach to developing an approximation theory for OOMs of infinite-dimensional processes. Building upon foundational work outlined in an unpublished tutorial [Jae98], an inner product structure on the space of future distributions is rigorously established and the continuity of observable operators with respect to the associated 2-norm is proven. The original theorem proven in this thesis describes a fundamental obstacle in making an infinite-dimensional space of future distributions into a Hilbert space. The presented findings lay the groundwork for future research in approximating observable operators of infinite-dimensional processes, while a remedy to the encountered obstacle is suggested.
Item Type: | Thesis (Bachelor's Thesis) |
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Supervisor name: | Jaeger, H. |
Degree programme: | Artificial Intelligence |
Thesis type: | Bachelor's Thesis |
Language: | English |
Date Deposited: | 08 Apr 2024 07:52 |
Last Modified: | 08 Apr 2024 07:52 |
URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/32215 |
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