论文标题
代数减少隐藏的马尔可夫模型
Algebraic Reduction of Hidden Markov Models
论文作者
论文摘要
通过使用系统理论方法来解决将隐藏的马尔可夫模型（HMM）减少到较小的维度之一的问题之一。实现理论工具通过利用合适的概率空间代数表示扩展到HMM。我们提出了两种算法，这些算法返回由随机投影运算符获得的粗粒等效的HMM：第一返回模型，这些模型精确地重现了给定输出过程的单个时间分布，而在第二个（多时间）分布中，则保留了第二个模型。减少方法不仅利用了观察到的输出的结构，而且还利用其初始条件，每当后者已知或属于给定的子类时。最佳算法是针对一类HMM（即可观察到的）得出的。
The problem of reducing a Hidden Markov Model (HMM) to one of smaller dimension that exactly reproduces the same marginals is tackled by using a system-theoretic approach. Realization theory tools are extended to HMMs by leveraging suitable algebraic representations of probability spaces. We propose two algorithms that return coarse-grained equivalent HMMs obtained by stochastic projection operators: the first returns models that exactly reproduce the single-time distribution of a given output process, while in the second the full (multi-time) distribution is preserved. The reduction method exploits not only the structure of the observed output, but also its initial condition, whenever the latter is known or belongs to a given subclass. Optimal algorithms are derived for a class of HMM, namely observable ones.
