## Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network (2002)

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Venue: | Proc. 1st IEEE Computer Society Bioinformatics Conference |

Citations: | 41 - 18 self |

### BibTeX

@ARTICLE{Imoto02bayesiannetwork,

author = {Seiya Imoto and Kim Sunyong and Takao Goto and Sachiyo Aburatani and Kousuke Tashiro and Satoru Kuhara and Satoru Miyano},

title = {Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network},

journal = {Proc. 1st IEEE Computer Society Bioinformatics Conference},

year = {2002},

volume = {1},

pages = {219--227}

}

### Years of Citing Articles

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### Abstract

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. A problem still remains to be solved in selecting an optimal graph, which gives the best representation of the system among genes. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes. 1.

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Citation Context ... However, the assumption that the parent genes depend linearly on the objective gene is not always guaranteed. Imoto et al. [22] proposed the use of nonparametric additive regression models (see also =-=[16, 18]-=-) for capturing not only linear dependencies but also nonlinear structures between genes. In this paper, we propose a method for constructing the genetic network by using Bayesian networks and the non... |

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Citation Context ...mentally. We investigate the graph selection problem as a statistical model selection or evaluation problem and theoretically derive a new criterion for choosing a graph using the Bayes approach (see =-=[6]-=-). The proposed criterion automatically optimizes all parameters in the model and gives the optimal graph. In addition, our proposed method includes the previous methods for constructing genetic netwo... |

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Citation Context ... large in a more complicated model. Hence, we need to consider the statistical approach based on the generalized or predictive error, Kullback-Leibler information, Bayes approach and so on (see e.g., =-=[1, 24, 25]-=- for the statistical model selection problem). In this section, we construct a criterion for evaluating a graph based on our model (5) from Bayes approach. The posterior probability of the graph is ob... |

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Citation Context ...ration (6). Heckerman and Geiger [20] used the conjugate priors for solving the integral and gave a closed-form solution. To compute this high dimensional integration, we use Laplace’s approximation =-=[9, 19, 31]-=- for integrals � �n f(xi; θG)π(θG|λ)dθG i=1 = (2π/n)r/2 |Jλ( ˆ θG)| 1/2 exp{nlλ( ˆ θG|Xn)}{1 + Op(n −1 )}, where r is the dimension of θG, lλ(θG|Xn) = � n i=1 log f(xi; θG)/n + log π(θG| λ)/n, Jλ(θG) ... |

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Citation Context ...100 genes. 1. Introduction Due to the development of the microarray technology, constructing genetic network receives a large amount of attention in the fields of molecular biology and bioinformatics =-=[3, 4, 5, 14, 15, 17, 22, 28]-=-. However, the dimensionality and complexity of the data disturb the progress of the microarray gene expression data analysis. That is to say, the information that we want is buried in a huge amount o... |

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Citation Context ... data with noise. In this paper, we propose a new statistical method for constructing a genetic network that can capture 219 even the nonlinear relationships between genes clearer. A Bayesian network =-=[7, 23]-=- is an effective method in modeling phenomena through the joint distribution of a large number of random variables. In recent years, some interesting works have been established in constructing geneti... |

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Citation Context ... However, the assumption that the parent genes depend linearly on the objective gene is not always guaranteed. Imoto et al. [22] proposed the use of nonparametric additive regression models (see also =-=[16, 18]-=-) for capturing not only linear dependencies but also nonlinear structures between genes. In this paper, we propose a method for constructing the genetic network by using Bayesian networks and the non... |

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Citation Context ...ndom variables. In recent years, some interesting works have been established in constructing genetic networks from microarray gene expression data by using Bayesian networks. Friedman and Goldszmidt =-=[12, 13, 14]-=- discretized the expression values and assumed multinomial distributions as the candidate statistical models. Pe’er et al. [28] investigated the threshold value for discretizing. On the other hand, Fr... |

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Citation Context ...100 genes. 1. Introduction Due to the development of the microarray technology, constructing genetic network receives a large amount of attention in the fields of molecular biology and bioinformatics =-=[3, 4, 5, 14, 15, 17, 22, 28]-=-. However, the dimensionality and complexity of the data disturb the progress of the microarray gene expression data analysis. That is to say, the information that we want is buried in a huge amount o... |

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Citation Context ...100 genes. 1. Introduction Due to the development of the microarray technology, constructing genetic network receives a large amount of attention in the fields of molecular biology and bioinformatics =-=[3, 4, 5, 14, 15, 17, 22, 28]-=-. However, the dimensionality and complexity of the data disturb the progress of the microarray gene expression data analysis. That is to say, the information that we want is buried in a huge amount o... |

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Citation Context ...ndom variables. In recent years, some interesting works have been established in constructing genetic networks from microarray gene expression data by using Bayesian networks. Friedman and Goldszmidt =-=[12, 13, 14]-=- discretized the expression values and assumed multinomial distributions as the candidate statistical models. Pe’er et al. [28] investigated the threshold value for discretizing. On the other hand, Fr... |

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Citation Context ...timated from the data. The resulted network strongly depends on their values. Then Friedman et al. [15] considered fitting linear regression models, which analyze the data in the continuous (see also =-=[20]-=-). However, the assumption that the parent genes depend linearly on the objective gene is not always guaranteed. Imoto et al. [22] proposed the use of nonparametric additive regression models (see als... |

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Citation Context ...bility of the graph, πG, πG = exp{−(No. of hyper parameters)} = p� exp{−(qj + 1)} = p� πLj . j=1 j=1 The justification of this prior is based on Akaike’s Bayesian information criterion, known as ABIC =-=[2]-=-, and Akaike’s information criterion, AIC [1]. 3.3. Criterion We derived the criterion, BNRChetero, for choosing the graph in a general framework. By using the equation (8), the BNRChetero score of th... |

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Citation Context ...ration (6). Heckerman and Geiger [20] used the conjugate priors for solving the integral and gave a closed-form solution. To compute this high dimensional integration, we use Laplace’s approximation =-=[9, 19, 31]-=- for integrals � �n f(xi; θG)π(θG|λ)dθG i=1 = (2π/n)r/2 |Jλ( ˆ θG)| 1/2 exp{nlλ( ˆ θG|Xn)}{1 + Op(n −1 )}, where r is the dimension of θG, lλ(θG|Xn) = � n i=1 log f(xi; θG)/n + log π(θG| λ)/n, Jλ(θG) ... |

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Citation Context ...-JBCB 00007 234 S. Imoto et al. To avoid this problem, we consider fitting a nonparametric regression model with heterogeneous error variances xij = mj1(p (j) i1 ) + · · · + mjqj (p (j) iqj ) + εij , =-=(2)-=- where εij depends independently and normally on mean 0 and variance σ 2 ij and mjk(·) is a smooth function from R to R. Here R denotes a set of real numbers. This model includes Imoto et al.’s model ... |

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Citation Context ... large in a more complicated model. Hence, we need to consider the statistical approach based on the generalized or predictive error, Kullback-Leibler information, Bayes approach and so on (see e.g., =-=[1, 24, 25]-=- for the statistical model selection problem). In this section, we construct a criterion for evaluating a graph based on our model (5) from Bayes approach. The posterior probability of the graph is ob... |

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Citation Context ...rve. (b1) and (c1): The effect of hyperparamter ρ j in the parameter of the error variances. This parameter can capture the heteroscedastisity of the data and can reduce the effects of outliers. GCN4 =-=[8, 11, 29]-=-. In this paper, we made clear that both genetic relation. Figure 4 indicates that those ADE genes and histidine biosynethesis genes are related with BAS1 more directly than GCN4. The ribose component... |

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Citation Context ...rve. (b1) and (c1): The effect of hyperparamter ρ j in the parameter of the error variances. This parameter can capture the heteroscedastisity of the data and can reduce the effects of outliers. GCN4 =-=[8, 11, 29]-=-. In this paper, we made clear that both genetic relation. Figure 4 indicates that those ADE genes and histidine biosynethesis genes are related with BAS1 more directly than GCN4. The ribose component... |

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Citation Context ... large in a more complicated model. Hence, we need to consider the statistical approach based on the generalized or predictive error, Kullback-Leibler information, Bayes approach and so on (see e.g., =-=[1, 24, 25]-=- for the statistical model selection problem). In this section, we construct a criterion for evaluating a graph based on our model (5) from Bayes approach. The posterior probability of the graph is ob... |

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Citation Context ...heteroscedastic regression criterion, named BNRChetero, for selecting a graph � � � �n BNRChetero(G) = −2 log πG f(xi; θG)π(θG|λ)dθG i=1 ≈ −2 log πG − r log(2π/n) + log |Jλ( ˆ θG)| − 2nlλ( ˆ θG|Xn) . =-=(6)-=-sNovember 5, 2003 23:27 WSPC/185-JBCB 00007 Nonlinear Modeling of Genetic Network 237 The optimal graph is chosen such that the criterion BNRChetero (6) is minimal. The merit of the use of the Laplace... |

1 | Estimation of genetic networks and functional 5, 2003 23:27 WSPC/185-JBCB 00007 250 S. Imoto et al. structures between genes by using Bayesian networks and nonparametric regression - Imoto, Goto, et al. - 2002 |

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Citation Context ...urve. (b1) and (c1): The effect of hyperparamter ρj in the parameter of the error variances. This parameter can capture the heteroscedastisity of the data and can reduce the effects of outliers. GCN4 =-=[8, 11, 29]-=-. In this paper, we made clear that both genetic relation. Figure 4 indicates that those ADE genes and histidine biosynethesis genes are related with BAS1 more directly than GCN4. The ribose component... |