## 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: | 38 - 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.

### Citations

2643 |
Estimating the dimension of a model
- Schwarz
- 1978
(Show Context)
Citation Context ... the criterion, BNRChetero, under the assumption log π(θG|λ) = O(n). If we use the prior density satisfying log π(θG|λ) = O(1), the BNRChetero score results in Schwarz’s criterion known as BIC or SIC =-=[30]-=-. In such case, the mode ˆ θG is equivalent to the maximum likelihood estimate. 3. Estimating Genetic Network 3.1. Nonparametric regression In this section we present the method for constructing genet... |

1574 | Generalized Additive Models
- Hastie, Tibshirani
- 1990
(Show Context)
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... |

1539 |
Information theory and an extension of the maximum likelihood principle
- Akaike
- 1992
(Show Context)
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... |

1358 |
Statistical decision theory and Bayesian analysis. (2nd Ed
- Berger
- 1985
(Show Context)
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... |

1229 |
A Practical Guide to Splines
- Boor
- 1978
(Show Context)
Citation Context ... practice based on the proposed method described above. First we would like to mention the nonparametric regression model. In the additive model, we construct each smooth function mjk(·) by B-splines =-=[10, 22]-=-. Figure 2 is an example of B-splines smoothed curve. The thin curves are B-splines that are weighted by coefficients and thick line is a smoothed curve that is obtained by the linear combination of w... |

1127 | A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9:309–347
- Cooper, Herskovits
- 1992
(Show Context)
Citation Context ...jk), where λjk are hyperparameters. We use a singular Mjk variate normal distribution as the prior distribution on γjk, � 2π πjk(γjk|λjk) = nλjk �−(Mjk−2)/2 |Kjk| 1/2 + exp � − nλjk 2 γT � jkKjkγjk , =-=(9)-=- where Kjk is an Mjk × Mjk symmetric positive semidefinite matrix satisfying γ T jk Kjkγjk = � Mjk α=3 (γ(j) αk − 2γ(j) α−1,k + γ(j) α−2,k )2 . Next we consider the prior probability of the graph πG. ... |

965 | An introduction to Bayesian Network - Jensen - 1996 |

948 | Learning Bayesian networks: The combination of knowledge and statistical data
- Heckerman, Geiger, et al.
- 1995
(Show Context)
Citation Context ... the construction of a suitable criterion becomes the center of attention of statistical genetic network modeling. Friedman and Goldszmidt [14] used the BDe criterion, which was originally derived by =-=[21]-=- for choosing a graph. The BDe criterion only evaluates the Bayesian network based on the multinomial distribution model and Dirichlet priors. However, Friedman and Goldszmidt [14] kept the unknown h... |

891 | A tutorial on learning with Bayesian networks
- Heckerman
- 1998
(Show Context)
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) ... |

792 | D (2000) Using Bayesian networks to analyze expression data
- Friedman, Linial, et al.
(Show Context)
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... |

661 |
Probabilistic Networks and Expert Systems
- Cowell, Dawid, et al.
- 1999
(Show Context)
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... |

509 |
Nonparametric Regression and Generalized Linear Models
- Green, Silverman
- 1994
(Show Context)
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... |

367 |
Model selection and inference: a practical information-theoretic approach
- Burnham, Anderson
- 1998
(Show Context)
Citation Context ...3). Choosing constants w1j, . . . , wnj is an important problem for capturing the heteroscedasticity of the data. In this paper, we set the weights wij = g(pij; ρj) = exp{−ρj�pij − ¯p j� 2 /2s 2 j} , =-=(8)-=- where ρj is a hyperparameter, ¯p j = � n i=1 pij/n and s 2 j = � n i=1 �pij − ¯p j� 2 /nqj. If we set ρj = 0, the weights are w1j = · · · = wnj = 1 and the model has homogeneous error variances. If w... |

243 | Learning Bayesian networks with local structure
- Friedman, Goldszmidt
- 1998
(Show Context)
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... |

221 |
Accurate approximations for posterior moments and marginal densities
- Tierny, Kadane
- 1986
(Show Context)
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) ... |

202 | Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. Pacific Symposium on Biocomputing 4
- Akutsu, Miyano, et al.
- 1999
(Show Context)
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... |

166 | Inferring Subnetworks from Perturbed Expression Profiles
- Pe'er, Regev, et al.
- 2001
(Show Context)
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... |

166 | Modeling gene expression data using dynamic Bayesian networks - Murphy, Mian - 1999 |

139 | Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks - Hartemink, Gifford, et al. - 2001 |

113 |
Hybrid Petri net representation of gene regulatory network’, Pac Symp Biocomput
- Matsuno, Doi, et al.
- 2000
(Show Context)
Citation Context ...s and heteroscedasticity of the expression data. If we have a network that represents the causal relationship among genes, we can simulate the genetic system on the computer, e.g., Genomic Object Net =-=[26, 27]-=-. In this stage, it is required that the relationships between genes are suitably estimated. In this sense, the proposed heteroscedastic model can give an essential rhosYKL060C FBA1 fuctose-biosphosph... |

103 | Combining location and expression data for principled discovery of genetic regulatory network models
- Hartemink, Gifford, et al.
- 2002
(Show Context)
Citation Context |

101 |
Inferring qualitative relations in genetic networks and metabolic pathways
- Akutsu, Miyano, et al.
(Show Context)
Citation Context |

98 | Miyano: Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. Pac Symp Biocomput175-86
- Imoto, Goto, et al.
- 2002
(Show Context)
Citation Context |

72 | The Estimation of Probabilities - Good - 1965 |

69 | Discretizing Continuous Attributes While Learning Bayesian Networks
- Friedman, Goldszmidt
- 1996
(Show Context)
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... |

65 | Inferring gene regulatory networks from time ordered gene expression data of Bacillus subtilis using differential equations - Hoon, Imoto, et al. - 2003 |

64 | Inference of a genetic network by a combined approach of cluster analysis and graphical Gaussian modeling - Toh, Horimoto - 2002 |

55 | Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data - Kim, Imoto, et al. - 2003 |

53 | Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint function
- Akutsu, Miyano, et al.
- 2000
(Show Context)
Citation Context |

44 | Learning Bayesian networks: A unification for discrete and Gaussian domains
- Heckerman, Geiger
- 1995
(Show Context)
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... |

39 |
Likelihood and the Bayes procedure. In
- Akaike
- 1980
(Show Context)
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... |

38 | Evaluating Functional Network Inference Using Simulations of Complex Biological Systems. (2002) Accepted by The 10th international conference on Intelligent Systems for Molecular Biology - Smith, Jarvis, et al. |

35 |
Coregulation of purine and histidine biosynthesis by the transcriptional activators
- Daignan-Fornier, Fink
- 1992
(Show Context)
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... |

31 | Maximum likelihood estimation of optimal scaling factors for expression array normalization - Hartemink, Gifford, et al. - 2001 |

27 | Generalized Additive Models.’ (Chapman and - Hastie, Tibshirani - 1990 |

25 | A Practical Guide to Splines, Springer-Verlag New-York - Boor - 1978 |

24 |
Likelihood and Bayes procedure, in Bayesian Statistics, edited by
- Akaike
- 1980
(Show Context)
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 ... |

22 |
Generalised information criteria in model selection
- Konishi, Kitagawa
- 1996
(Show Context)
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... |

22 | A Self-Organizing State Space Model - Kitagawa - 1998 |

20 | S.: XML documentation of biopathways and their simulations - Matsuno, Doi, et al. - 2001 |

17 |
Approximate predictive likelihood
- Davison
- 1986
(Show Context)
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) ... |

14 |
Translation of the yeast transcriptional activator GCN4 is stimulated by purine limitation: implications for activation of the protein kinase GCN2
- Rolfes, Hinnebusch
- 1993
(Show Context)
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... |

6 |
Role of the Myb-like protein Bas1p in Saccharomyces cerevisiae: a proteome analysis
- Denis, Boucherie, et al.
- 1998
(Show Context)
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... |

6 |
Statistical model evaluation and information criteria
- Konishi
- 1999
(Show Context)
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... |

5 | Knowledge Discovery and Self-Organizing State Space Model - Higuchi, Kitagawa - 2000 |

4 | Variance stablization applied to microarray data calibration and to quantification of differential expression - Huber, Heydebreck, et al. |

3 | A variancestabilizing transformation from gene-expression microarray data - Durbin, Hardin, et al. - 2002 |

2 |
Estimating nonlinear regression models based on radial basis function networks (in Japanese
- Ando, Imoto, et al.
- 2001
(Show Context)
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 |

1 |
Monribot and B. Daignan-Fornier.Role of the Myb-like protein Bas1p in Saccharomycescerevisiae: a proteome analysis
- Denis, Boucherie, et al.
- 1998
(Show Context)
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... |