Quadratic Observable Operator Models for efficient prediction and classification of stochastic time series

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Hidden Markov Models (HMMs) are the core modelling method in speech recognition systems and are increasingly employed in biosequence analysis. Their main drawbacks are slow learning algorithms and suboptimal models due to the local optimization character of known learning algorithms. Observable operator models (OOMs) are a recently developed alternative to HMMs whose associated, novel learning algorithm needs only a fraction of learning time, yields more accurate models, and is asymptotically correct (finds the global optimimum). One drawback of OOMs that has prevented their widespread use so far is that they may predict negative values for probabilities. The proposed project investigated quadratic and norm-OOMs, in which non-negativity of predicted probabilities is guaranteed by design. In the first two years of funding (the project is now in month 19/24) the basic mathematical theory of quadratic and norm-OOMs was established and learning algorithms (of an altogether novel kind) were developed and tested on synthetic datasets; all meeting and surpassing the originally envisioned goals.