Dixit Purushottam D
Department of Systems Biology, Columbia University, New York, NY 10032, U.S.A.
Neural Comput. 2019 May;31(5):980-997. doi: 10.1162/neco_a_01184. Epub 2019 Mar 18.
Stochastic kernel-based dimensionality-reduction approaches have become popular in the past decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, based on our previous work on inference of Markov models, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.
基于随机核的降维方法在过去十年中变得流行起来。许多此类方法的核心组件是一个对称核，它量化数据点对之间的邻近程度以及数据上的核诱导马尔可夫链。通常，马尔可夫链通过行归一化由核完全指定。然而，在许多情况下，希望对马尔可夫链施加用户指定的稳态和动态约束。不幸的是，不存在用于施加此类用户定义约束的系统框架。在此，基于我们之前关于马尔可夫模型推断的工作，我们引入一种基于路径熵最大化的方法，以使用核和额外的用户指定约束来推导马尔可夫链的转移概率。我们通过示例说明这些马尔可夫链的有用性。
