论文标题
最大马尔可夫链
Max Markov Chain
论文作者
论文摘要
在本文中，我们介绍了Max Markov链（MMC），这是一种有用的高阶马尔可夫链（HMC）的新颖表示形式，各州之间的相关性稀疏。 MMC在保留HMC的表现力的同时是简约的。即使与HMC近似模型一样，参数优化通常是棘手的，它具有分析解决方案，更好的样品效率以及比HMC和近似HMC的所需空间和计算优势。正如我们在经验上所显示的那样，同时存在这种类型的链的有效近似解决方案，这使MMC可以扩展到HMC和近似HMC难以执行的大型域。我们将MMC与HMC，一阶Markov链和具有各种数据类型的合成域中的近似HMC模型进行了比较，以证明MMC是建模随机过程并具有许多潜在应用的宝贵替代方法。
In this paper, we introduce Max Markov Chain (MMC), a novel representation for a useful subset of High-order Markov Chains (HMCs) with sparse correlations among the states. MMC is parsimony while retaining the expressiveness of HMCs. Even though parameter optimization is generally intractable as with HMC approximate models, it has an analytical solution, better sample efficiency, and the desired spatial and computational advantages over HMCs and approximate HMCs. Simultaneously, efficient approximate solutions exist for this type of chains as we show empirically, which allow MMCs to scale to large domains where HMCs and approximate HMCs would struggle to perform. We compare MMC with HMC, first-order Markov chain, and an approximate HMC model in synthetic domains with various data types to demonstrate that MMC is a valuable alternative for modeling stochastic processes and has many potential applications.
