Investigation on the Applicability of Observable Operator Models for Nonstationary Processes using Multiplicity Automata

Executive Summary Observable Operator Models (OOM) are statistical tools developed in the field of Machine Learning with the purpose of modelling certain classes of stochastic processes. They have been highly successful, both in terms of efficiency and accuracy of results, compared to the more widely-used Hidden Markov Models (HMM), when used on stationary symbol sequences. For symbol sequences which are not stationary, however, mechanisms have to be investigated through which these sequences can be used as training data, and also the current algorithms have to be modified accordingly. Thus the extension of OOM range of applicability would be of prime importance, since the power of OOM would be readily available to fields where modelling nonstationary sequences plays the most important role, such as biosequence analysis or speech recognition. The first steps in this direction, namely of extending basic learning algorithms for finite sequences have been undertaken by Dan Alistarh in his thesis in Spring 2007. My research focuses on finding a good representations of finite sequences, by using Multiplicity Automata, tools initially devised in Learning Theory. First, a mathematical framework has been established, which generalizes the existing theory, and then, it is mentioned how this integrates with previous research done in the field.