Abstract Hidden Markov Models: A Monadic Account of Quantitative Information Flow
Abstract Hidden Markov Models: A Monadic Account of Quantitative Information Flow
复制标题
抽象隐马尔可夫模型：定量信息流的一元论
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
T. Rabehaja
中科院分区：
文献类型：
--
作者：
Annabelle McIver;Carroll Morgan;T. Rabehaja
隐马尔可夫模型（HMM）是马尔可夫过程的数学模型，其状态是隐藏的，但信息可以通过通道泄漏。它们通常表示为三向联合概率分布。我们使用HMM作为概率隐藏状态序列程序的表示法，将它们重新转换为“抽象”HMM，即在Giry monad D中进行计算，并为它们配置增加安全性的偏阶。然而，为了对一元类型进行编码，隐藏在状态X上，我们使用DX→D2X而不是传统的X→DX。我们用一个非常小的Haskell原型来说明这个构造。然后，我们将不确定性测度作为现有概率熵多样性的概括，并提出它们的特征解析性质。在此基础上，我们给出了HMM的“向后”、不确定性转换语义，对偶于“向前”抽象HMM。最后，我们将统计数据库的Dalenius期望作为语义组合性的一个问题进行了讨论，并提出了一种考虑它的方法。
Hidden Markov Models, HMM's, are mathematical models of Markov processes whose state is hidden but from which information can leak via channels. They are typically represented as 3-way joint probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs, after recasting them as “abstract” HMM's, i.e. computations in the Giry monad D, and equipping them with a partial order of increasing security. However to encode the monadic type with hiding over state X we use DX→D2X rather than the conventional X→DX. We illustrate this construction with a very small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, and we propose characteristic analytic properties for them. Based on that, we give a “backwards”, uncertainty-transformer semantics for HMM's, dual to the “forwards” abstract HMM's. Finally, we discuss the Dalenius desideratum for statistical databases as an issue in semantic compositionality, and propose a means for taking it into account.
DOI：
--
发表时间：
2000
期刊：
--
影响因子：
--
作者：
Dan Jurafsky;James H. Martin
通讯作者：
Dan Jurafsky;James H. Martin