Nonlinear modeling of gene networks from time series gene expression data
A technology of gene network and gene expression, which is applied in the field of inferring the optimal network relationship by the minimization standard, namely BNRCdynamic, can solve problems such as the inability to fully solve the cycle regulation network
- Summary
- Abstract
- Description
- Claims
- Application Information
AI Technical Summary
Problems solved by technology
Method used
Image
Examples
example 1
[0039] Example 1: Bayesian Networks and Nonlinear Regression
[0040] Suppose we have an n × p microarray gene expression data matrix X, where n and p are the number of microarrays and genes, respectively. Usually, the number p of genes is much larger than the number n of microarrays. In gene network estimation based on Bayesian network, genes are regarded as random variables. When we simulate a gene network by using a statistical model described by a density or probability function, the statistical model should include p random variables. However, we only have n samples, and n is usually much smaller than p. In this case, inference of the pattern is very difficult or impossible because the model has many parameters and the number of samples is not enough to estimate these parameters. Bayesian models have been suggested in such simulations.
[0041] In the context of Dynamic Bayesian Networks, we consider time series data, and the ith column vector x of X i corresponds to...
example 2
[0064] Example 2: Obtaining criteria for selecting a network
[0065] When we fix the network structure, the dynamic Bayesian network and nonparametric regression models introduced in the previous section can be constructed and estimated by a suitable procedure. However, the gene network is usually unknown, and we should estimate the optimal network from the data. This problem can be viewed as a statistical model selection problem (see Akaike [1]; Konishi and Kitagawa [17]; Burnham and Anderson [4]; Konishi [16]). We address this issue from a Bayesian statistical approach and derive criteria for evaluating the benefits of dynamic Bayesian networks and nonparametric regression models.
[0066] Assuming that in dynamic Bayesian networks and nonparametric regression models π(θ G |λ) is about θ G The prior distribution of the parameters, and assume that π(θ G |λ)=O(n). This marginal likelihood can be expressed as
[0067] ∫f(X 11 ,...,X np ; G )π(θ G |λ)dθ G .
[0068]...
example 3
[0079] Example 3: Estimation of Gene Networks
[0080] In this section, we show specific strategies for estimating gene networks from cDNA microarray time-series gene expression data.
[0081] 3.1 Nonlinear regression
[0082] We use the elementary function approach to construct the smooth function m described in Section 2 jk (·). In this paper we use B-splines (de Boor [7]) as basis functions. De Boor's algorithm (de Boor [7], Chapter 10, p. 130 (3)) is a useful method for computing B-splines of arbitrary order. We use 20 B-splines with equidistant knots (see also Dierckx [10]; Eilter and Marx [11] for details on B-splines).
[0083] 3.2 About the prior distribution of the parameters in the model
[0084] For the prior distribution of parameters θG, suppose the parameter vector θ j are independent of each other, then the prior distribution can be decomposed into π j ( θ G ...
PUM
Login to View More Abstract
Description
Claims
Application Information
Login to View More