Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs.
Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs.
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DOI：
10.1186/2190-8567-4-6
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发表时间：
2014-04-17
影响因子：
2.3
通讯作者：
Thomas PJ
中科院分区：
文献类型：
--
作者：
Schmidt DR;Thomas PJ
细胞生理机制的数学模型通常涉及代表功能状态网络内转变的图上的随机游走。 Schmandt 和 Galán 最近引入了一种新颖的随机屏蔽近似，作为一种快速、准确的方法，用于从有限状态马尔可夫过程生成近似样本路径，其中只能观察到状态的子集。例如，在离子通道模型中，例如霍奇金-赫胥黎或其他基于电导的神经模型，神经细胞具有一群离子通道，其状态构成图的节点，其中只有一些允许跨膜电流通过。随机屏蔽近似包括忽略与图中边缘相关的动态波动，不直接影响可观察状态。我们考虑找到从图上的随机过程到较小样本空间上的近似过程的最佳复杂性降低映射的问题，这由图上特定线性测量函数的选择来确定。将离子通道状态分为导电状态和非导电状态提供了一个恰当的例子。除了确定 Schmandt 和 Galán 的近似在特定意义上实际上是最优的之外，我们还使用随机矩阵理论的最新结果来提供启发式误差估计，以评估随机图集合的随机屏蔽近似的准确性。此外，我们提供了一种新颖的定量方法来衡量反应图中各个转变对近似过程准确性的贡献。
Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin–Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán’s approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.