生物网络的结构辨识与参数估计
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摘要
本研究采用工程学和系统科学方法,分别以离散一阶线性、离散二阶线性、离散非线性、连续非线性、连续-离散非线性状态空间模型框架对动态生物网络进行了描述,并对生物网络的结构辨识和参数估计方法进行了探索,这为环境和药物干扰下系统动态特性分析及其控制研究奠定了基础。具体内容如下:
(1)提出和发展了约束性扩展卡尔曼滤波。网络结构约束是基因网络的参数估计区别于工程技术中的参数估计的显著标志。在工程技术领域中,我们一般不考虑系统的结构,但是基因网络是有结构的。有的基因之间具有相互作用,有的基因之间没有相互作用。基因网络参数估计算法中必须包含网络结构性约束。
(2)与Hao Xiong和Yoonsuck(2008)合作独立提出了调控网络的二阶线性状态空间模型。发展了用扩展卡尔曼滤波估计基因网络的二阶线性状态空间模型。基于芯片表达数据的调控网络通常采用一阶线性状态空间模型。针对调控网络,Hao和Yoonsuck用EM算法估计二阶线性模型的参数,而我们用扩展卡尔曼滤波来估计同样模型的参数。
(3)把扩展卡尔曼滤波用于非线性代谢网络、信号转导网络的动力学方程的参数估计,发展了可用于一般非线性动态系统的扩展卡尔曼滤波参数估计方法。
(4)提出用Rao-blackwellised粒子滤波对非线性生物网络进行参数估计。
(5)生物网络一般为具有离散观测数据的连续动态系统。这种生物网络更适合用混合非线性状态空间模型来描述。我们尝试估计这类混合非线性模型的生物网络的参数,发展了连续-离散非线性状态空间模型参数估计算法,并将其应用于JAK-STAT信号转导通路。
(6)信号转导网络和基因调控网络的数据多数是多次实验的面板数据。目前还没有现成的针对面板数据的参数估计算法。本研究发展处理面板数据的参数估计方法,将采样数写入状态空间模型,并对扩展卡尔曼滤波算法和Rao-Blackwellised粒子滤波算法重新进行推导。
(7)发展了新的EKF_EM混合算法:以EKF方法同时估计状态和参数,同时采用EM算法估计系统噪音协方差矩阵和观测噪音协方差矩阵。算法精度得到一定程度的提高。
(8)首次采用分布估计算法搜索流行病数据的动态模型,并与遗传算法进行比较,发展了与遗传算法或分布估计算法结合的扩展卡尔曼滤波算法。
Our study focused on developing methods to recognize the biological network and estimate its parameters. Identification of the dynamic biological networks is a tough but vital work. Without the estimated parameters in the identification of dynamic biological networks, any quantitative analysis of the biological process could not be implemented. Up to date, little related work has been reported in the literature, except of the existing methods used in simple applications. The methods have not been developed corresponding to biological networks identification and parameter estimation. State-space approach to modelling biological networks is presented in this report. We are mainly devoted to the following eight aspects on structure identification and parameters estimation:
(1) We put forward and develop extended kalman filter with structural constraints. Structural constraints are the main distinctive characteristics during applying extended kalman filter algorithm in genetic networks area and in engineering technology area. The latter usually has not been taken into account in structural information. However, genetic networks have structural information. For example, there are mutual interactions between some genes, but they may be not between others. Structural constraints can help trim the number of parameters that need estimate and alleviate over-fitting, which are especially acute given the limited amount of data we have.
(2) Hao Xiong and we cooperatively and independently develop a second-order dynamics model in genetic networks and present the extended kalman filter to estimate the parameters in the second-order linear state-space model for gene regulation networks. The Gene regulation networks based on microarray gene expression profile data are usually adopted one-order linear state-space model. Hao and Yoonsuck used expectation maximization (EM) to estimate the parameters in the second-order linear state-space model for gene regulation networks, while we implement the extended kalman filter to estimate the parameters in second-order linear state-space model for gene regulation networks.
(3) This is the first study to use the iterated extended kalman filter to estimate the parameters in nonlinear state-space model for biological networks and to develop extended kalman filter to estimate the parameter in general nonlinear state-space model for biological networks.
(4) We are the first one to propose rao-blackwellised particle filter algorithm to estimate the parameters in nonlinear state-space model for biological networks, and also the first one to adopt rao-blackwellised particle filter algorithm to estimate the parameter in general nonlinear dynamic system.
(5) This is the first time to implement continuous-time extended kalman filter for linear and nonlinear continuous-time dynamics with continuous-time measurements in the biological networks. We program the Hybrid extended kalman filter for linear and nonlinear continuous-time dynamics with discrete-time measurements in biology networks.
(6) We deal with panel data in our parameter estimation algorithm. Multiple samples in the time-course data are seldom appeared in engineer application but it is common in biology data. So, we incorporate multiple samples into the state-space equation. Since mathematical model becomes more complex, the derived process of EKF and RBPF algorithm were more difficult. We finished all programs and had the absolute patent right.
(7) This is the first study to use EM algorithm to estimate system noise covariance Q and measurement noise covariance R during adopting extend kalman filter to estimate the parameter in nonlinear dynamical state-space models for gene regulation and signal transduction networks. Since the state and state error covariance in the EKF depend on the initial values of parameters system noise covariance Q and the measurement noise covariance R. Thus, we consider a simple recursive procedure for estimation of the parameters Q and R. the precision of the algorithm is greatly improved.
(8) We use the estimation of distribution algorithm for the first time to search the networks of epidemic disease data and compare it with genetic algorithm. Experiment results showed that the estimation of distribution algorithm has the following advantages: fast convergence speed, consume little time, easy to obtain the optimal solution and do not destroy the relationships between the variables.
(1)提出和发展了约束性扩展卡尔曼滤波。网络结构约束是基因网络的参数估计区别于工程技术中的参数估计的显著标志。在工程技术领域中,我们一般不考虑系统的结构,但是基因网络是有结构的。有的基因之间具有相互作用,有的基因之间没有相互作用。基因网络参数估计算法中必须包含网络结构性约束。
(2)与Hao Xiong和Yoonsuck(2008)合作独立提出了调控网络的二阶线性状态空间模型。发展了用扩展卡尔曼滤波估计基因网络的二阶线性状态空间模型。基于芯片表达数据的调控网络通常采用一阶线性状态空间模型。针对调控网络,Hao和Yoonsuck用EM算法估计二阶线性模型的参数,而我们用扩展卡尔曼滤波来估计同样模型的参数。
(3)把扩展卡尔曼滤波用于非线性代谢网络、信号转导网络的动力学方程的参数估计,发展了可用于一般非线性动态系统的扩展卡尔曼滤波参数估计方法。
(4)提出用Rao-blackwellised粒子滤波对非线性生物网络进行参数估计。
(5)生物网络一般为具有离散观测数据的连续动态系统。这种生物网络更适合用混合非线性状态空间模型来描述。我们尝试估计这类混合非线性模型的生物网络的参数,发展了连续-离散非线性状态空间模型参数估计算法,并将其应用于JAK-STAT信号转导通路。
(6)信号转导网络和基因调控网络的数据多数是多次实验的面板数据。目前还没有现成的针对面板数据的参数估计算法。本研究发展处理面板数据的参数估计方法,将采样数写入状态空间模型,并对扩展卡尔曼滤波算法和Rao-Blackwellised粒子滤波算法重新进行推导。
(7)发展了新的EKF_EM混合算法:以EKF方法同时估计状态和参数,同时采用EM算法估计系统噪音协方差矩阵和观测噪音协方差矩阵。算法精度得到一定程度的提高。
(8)首次采用分布估计算法搜索流行病数据的动态模型,并与遗传算法进行比较,发展了与遗传算法或分布估计算法结合的扩展卡尔曼滤波算法。
Our study focused on developing methods to recognize the biological network and estimate its parameters. Identification of the dynamic biological networks is a tough but vital work. Without the estimated parameters in the identification of dynamic biological networks, any quantitative analysis of the biological process could not be implemented. Up to date, little related work has been reported in the literature, except of the existing methods used in simple applications. The methods have not been developed corresponding to biological networks identification and parameter estimation. State-space approach to modelling biological networks is presented in this report. We are mainly devoted to the following eight aspects on structure identification and parameters estimation:
(1) We put forward and develop extended kalman filter with structural constraints. Structural constraints are the main distinctive characteristics during applying extended kalman filter algorithm in genetic networks area and in engineering technology area. The latter usually has not been taken into account in structural information. However, genetic networks have structural information. For example, there are mutual interactions between some genes, but they may be not between others. Structural constraints can help trim the number of parameters that need estimate and alleviate over-fitting, which are especially acute given the limited amount of data we have.
(2) Hao Xiong and we cooperatively and independently develop a second-order dynamics model in genetic networks and present the extended kalman filter to estimate the parameters in the second-order linear state-space model for gene regulation networks. The Gene regulation networks based on microarray gene expression profile data are usually adopted one-order linear state-space model. Hao and Yoonsuck used expectation maximization (EM) to estimate the parameters in the second-order linear state-space model for gene regulation networks, while we implement the extended kalman filter to estimate the parameters in second-order linear state-space model for gene regulation networks.
(3) This is the first study to use the iterated extended kalman filter to estimate the parameters in nonlinear state-space model for biological networks and to develop extended kalman filter to estimate the parameter in general nonlinear state-space model for biological networks.
(4) We are the first one to propose rao-blackwellised particle filter algorithm to estimate the parameters in nonlinear state-space model for biological networks, and also the first one to adopt rao-blackwellised particle filter algorithm to estimate the parameter in general nonlinear dynamic system.
(5) This is the first time to implement continuous-time extended kalman filter for linear and nonlinear continuous-time dynamics with continuous-time measurements in the biological networks. We program the Hybrid extended kalman filter for linear and nonlinear continuous-time dynamics with discrete-time measurements in biology networks.
(6) We deal with panel data in our parameter estimation algorithm. Multiple samples in the time-course data are seldom appeared in engineer application but it is common in biology data. So, we incorporate multiple samples into the state-space equation. Since mathematical model becomes more complex, the derived process of EKF and RBPF algorithm were more difficult. We finished all programs and had the absolute patent right.
(7) This is the first study to use EM algorithm to estimate system noise covariance Q and measurement noise covariance R during adopting extend kalman filter to estimate the parameter in nonlinear dynamical state-space models for gene regulation and signal transduction networks. Since the state and state error covariance in the EKF depend on the initial values of parameters system noise covariance Q and the measurement noise covariance R. Thus, we consider a simple recursive procedure for estimation of the parameters Q and R. the precision of the algorithm is greatly improved.
(8) We use the estimation of distribution algorithm for the first time to search the networks of epidemic disease data and compare it with genetic algorithm. Experiment results showed that the estimation of distribution algorithm has the following advantages: fast convergence speed, consume little time, easy to obtain the optimal solution and do not destroy the relationships between the variables.
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