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

隐马尔可夫模型（hmm）是语音识别系统的核心建模方法，在生物序列分析中得到越来越多的应用。它们的主要缺点是学习算法缓慢和由于已知学习算法的局部优化特性而导致的次优模型。可观察算子模型（OOMs）是最近发展起来的hmm的替代方案，其相关的新颖学习算法只需要一小部分学习时间，产生更准确的模型，并且是渐进正确的（找到全局最优）。迄今为止，oom的一个缺点阻碍了它们的广泛使用，那就是它们可能会预测概率的负值。该方案研究了二次型和norm-OOMs，其中通过设计保证了预测概率的非负性。在资助的头两年（该项目目前在19/24月），建立了二次和norm-OOMs的基本数学理论，开发了学习算法（一种全新的算法）并在合成数据集上进行了测试；一切都达到并超越了最初设想的目标。

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.