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Bayesian robustness in the control of gene regulatory networks
 Signal Processing, IEEE Transactions on 2009
"... Abstract—The errors originating in the data extraction process, gene selection and network inference prevent the transition probabilities of a gene regulatory network from being accurately estimated. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention ..."
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Abstract—The errors originating in the data extraction process, gene selection and network inference prevent the transition probabilities of a gene regulatory network from being accurately estimated. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention strategy and to design robust intervention strategies. Two major approaches applied to the design of robust policies in general are the minimax (worst case) approach and the Bayesian approach. The minimax control approach is typically conservative because it gives too much importance to the scenarios which hardly occur in practice. Consequently, in this paper, we formulate the Bayesian approach for the control of gene regulatory networks. We characterize the errors emanating from the data extraction and inference processes and compare the performance of the minimax and Bayesian designs based on these uncertainties. Index Terms—Bayesian robustness, gene regulatory networks, intervention, parameter estimation, robust control. I.
FiniteHorizon Control of Genetic Regulatory Networks with Multiple HardConstraints
"... Abstract Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying the interactions among different genes while allowing uncertainty. This paper deals with the issue of finitehorizon control with multiple hardconstraints in a PBN. More precisely, under the constraint of the numb ..."
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Abstract Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying the interactions among different genes while allowing uncertainty. This paper deals with the issue of finitehorizon control with multiple hardconstraints in a PBN. More precisely, under the constraint of the number of times that each control method can be applied, we develop a control strategy by which the state of a given genetic network falls into a desired state set with a prescribed minimum probability. We propose an efficient algorithm to find the feasible solutions. An upper bound for the computational cost is also given. An numerical experiment is then conducted to demonstrate the efficiency of our proposed method.
A Heuristic Method for Generating Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix
, 2008
"... Abstract Probabilistic Boolean Networks (PBNs) have received much attention for modeling genetic regulatory networks. In this paper, we propose efficient algorithms for constructing a probabilistic Boolean network when its transition probability matrix is given. This is an important inverse problem ..."
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Abstract Probabilistic Boolean Networks (PBNs) have received much attention for modeling genetic regulatory networks. In this paper, we propose efficient algorithms for constructing a probabilistic Boolean network when its transition probability matrix is given. This is an important inverse problem in network inference from steadystate data, as most microarray data sets are assumed to be obtained from sampling the steadystate.
A Genetic Algorithm for Optimal Control of Probabilistic Boolean Networks
, 2008
"... Abstract We study the problem of finding optimal control policies for Probabilistic Boolean Networks (PBNs). Boolean Networks (BNs) and PBNs are effective tools for modeling genetic regulatory networks. A PBN is a collection of BNs driven by a Markov chain process. It is wellknown that the control/ ..."
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Abstract We study the problem of finding optimal control policies for Probabilistic Boolean Networks (PBNs). Boolean Networks (BNs) and PBNs are effective tools for modeling genetic regulatory networks. A PBN is a collection of BNs driven by a Markov chain process. It is wellknown that the control/intervention of a genetic regulatory network is useful for avoiding undesirable states associated with diseases like cancer. The optimal control problem can be formulated as a probabilistic dynamic programming problem. However, due to the curse of dimensionality, the complexity of the problem is huge. The main objective of this paper is to introduce a Genetic Algorithm (GA) approach for the optimal control problem. Numerical results are given to demonstrate the efficiency of our proposed GA method.
WaiKi Ching
"... Abstract—The construction and control of genetic regulatory networks using gene expression data is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the ..."
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Abstract—The construction and control of genetic regulatory networks using gene expression data is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN. The new model can preserve the strength of PBNs and at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are then given to demonstrate the effectiveness of our proposed model and control policy. I.
Chinese Academy of Sciences
"... The dependency propagation problem is to determine, given a view defined on data sources and a set of dependencies on the sources, whether another dependency is guaranteed to hold on the view. This paper investigates dependency propagation for recently proposed conditional functional dependencies (C ..."
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The dependency propagation problem is to determine, given a view defined on data sources and a set of dependencies on the sources, whether another dependency is guaranteed to hold on the view. This paper investigates dependency propagation for recently proposed conditional functional dependencies (CFDs). The need for this study is evident in data integration, exchange and cleaning since dependencies on data sources often only hold conditionally on the view. We investigate dependency propagation for views defined in various fragments of relational algebra, CFDs as view dependencies, and for source dependencies given as either CFDs or traditional functional dependencies (FDs). (a) We establish lower and upper bounds, all matching, ranging from ptime to undecidable. These not only provide the first results for CFD propagation, but also extend the classical work of FD propagation by giving new complexity bounds in the presence of finite domains. (b) We provide the first algorithm for computing a minimal cover of all CFDs propagated via SPC views; the algorithm has the same complexity as one of the most efficient algorithms for computing a cover of FDs propagated via a projection view, despite the increased expressive power of CFDs and SPC views. (c) We experimentally verify that the algorithm is efficient. 1.
1.1 Boolean Networks
"... Modeling genetic networks is an important in problem genomic research. Boolean Net work (BN) and its extension Probabilistic Boolean networks (PBN) have been proposed to model genetic regulatory interactions. In a PBN, its steadystate distribution gives very important information about the longru ..."
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Modeling genetic networks is an important in problem genomic research. Boolean Net work (BN) and its extension Probabilistic Boolean networks (PBN) have been proposed to model genetic regulatory interactions. In a PBN, its steadystate distribution gives very important information about the longrun behavior of the network. The construction of PBNs from a given transition probability matrix and a given set of BNs is an inverse problem of huge size. We propose a maximum entropy approach for the above problem. Newton’s method in conjunction with conjugate gradient method is then applied to solving the inverse problem. We investigate the convergence rate of the proposed method. Numerical examples are also given to demonstrate the effectiveness of our proposed algorithm.