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Towards an Approximation Theory of Observable Operator Models

Anyszka, Wojciech (2024) Towards an Approximation Theory of Observable Operator Models. Bachelor's Thesis, Artificial Intelligence.


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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 Building upon foundational work outlined in an unpublished tutorial [Jae98], an inner product structure on the space of future distributions is rigorously established and the continuity of observable operators with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)
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

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