We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more common version where each observation is drawn from a finite alphabet. We prove that one can determine in polynomial time whether two Hidden Markov Models with continuous observations are equivalent.

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具有连续观测值的隐马尔可夫模型的等价性

我们考虑隐马尔可夫模型，它发出从连续分布中提取的观察序列。例如，这样的模型可能会发出一个数字序列，每个数字都是从均匀分布中抽取出来的，但是均匀分布的支持度取决于隐马尔可夫模型的状态。这些模型概括了更常见的版本，其中每个观察值都来自有限的字母表。我们证明可以在多项式时间内确定两个具有连续观测值的隐马尔可夫模型是否等价。