Linear convergence of CQ algorithms and applications in gene regulatory network inference
Linear convergence of CQ algorithms and applications in gene regulatory network inference
复制标题
CQ算法的线性收敛及其在基因调控网络推理中的应用
DOI：
10.1088/1361-6420/aa6699
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发表时间：
2017
期刊：
影响因子：
2.1
通讯作者：
Yao Jen-Chih
中科院分区：
文献类型：
--
作者：
Wang Jinhua;Hu Yaohua;Li Chong;Yao Jen-Chih
在本文中，我们考虑的变步长CQ算法解决分裂可行性问题的Hilbert空间，研究线性收敛问题，并探讨在系统生物学中的应用。特别地，我们对分裂可行性问题引入了有界线性正则性的概念，并利用它建立了变步长CQ算法在使用适当步长类型时的线性收敛性，这涵盖了CQ算法文献中使用的大多数步长类型.我们还给出了保证这种有界线性正则性的一些温和的充分条件，并在此基础上给出了变步长CQ算法在许多应用场合下的线性收敛速度。据我们所知，这是第一个研究CQ算法的线性收敛速度的工作。在应用方面，我们考虑了系统生物学中的基因调控网络推理，将其表述为一个群Dantzig选择器，然后将其转化为一个分裂可行性问题。对小鼠胚胎干细胞基因表达数据的数值研究表明，变步长CQ算法适用于基因调控网络的推理，可以得到与生物学标准相匹配的可靠解。
In the present paper, we consider the varying stepsize CQ algorithm for solving the split feasibility problem in Hilbert spaces, investigate the linear convergence issue and explore an application in systems biology. In particular, we introduce a notion of bounded linear regularity property for the split feasibility problem, and use it to establish the linear convergence property for the varying stepsize CQ algorithm when using some suitable types of stepsizes, which covers most types of stepsizes used in the literature of CQ algorithms. We also provide some mild sufficient conditions for ensuring this bounded linear regularity property, and then conclude the linear convergence rate of the varying stepsize CQ algorithm for many application cases. To the best of our knowledge, this is the first work to study the linear convergence rate of CQ algorithms. In the aspect of application, we consider the gene regulatory network inference arising in systems biology, which is formulated as a group Dantzig selector and then cast into a split feasibility problem. The numerical study on gene expression data of mouse embryonic stem cell shows that the varying stepsize CQ algorithm is applicable to gene regulatory network inference in the sense that it obtains a reliable solution matching with biological standards.