Several researchers have focused on the inference of genetic networks. A number of genetic network inference methods have therefore been proposed. Among them, the inference methods that use the random forest show promise. Through the numerical experiment with the random-forest-based inference method, we found that its performance is improved by assigning appropriate weight values to gene expression data. In our earlier work, according to this experimental fact, we proposed “the guidelines for determining weight parameters.” We can improve the performance of the random-forest-based inference method using the weight values determined according to the guidelines. As the guidelines are qualitative, however, it is difficult to determine values for the weight parameters uniquely. In this study, we thus propose a new quantitative weighting method. The proposed method determines the weight values only on the basis of the similarity between measurements. Through the numerical experiments, we finally show that the weight values determined by the proposed weighting method are likely to make the performance of the random-forest-based inference method better.

Genetic network inference methods using random forests have shown promise. Some of the random-forest-based inference methods have an ability to analyze both time-series and static gene expression data. We think however that, as the gene expression levels at two adjacent measurements of a time-series data are often similar to each other, the gene expression levels at each measurement in the time-series data are less informative than those in the static data. On the basis of this idea, we proposed a new inference method that relies more on static gene expression data than time-series ones. Through the numerical experiments, we showed that the quality of the inferred genetic network is slightly improved by giving greater importance to static data than time-series ones. Although we develop the new method by modifying the random-forest-based inference method proposed by the authors, we could introduce the idea in this study into any inference method that is capable of analyzing both time-series and static gene expression data.

Huynh-Thu and colleagues initially introduce the random forest into field of genetic network inference. Their method, GENIE3, has performed well on genetic network inference problems. However, GENIE3 was designed only for analyzing static expression data that were measured under steady-state conditions. In order to infer genetic networks from time-series of gene expression data, this study proposes a new method based on the random forest. The proposed method has an ability to analyze both static and time-series data. When inferring a genetic network only from steady-state gene expression data, however, the proposed method is equivalent to GENIE3. Therefore, the proposed method can be seen as an extension of GENIE3. Through numerical experiments, we showed that the proposed method outperformed the existing inference methods on all of the 5 artificial genetic network inference problems.

In order to analyze short time-series of expression levels of many genes, we can use some clustering technique to identify genes with similar expression patterns, group them together, and then infer a network consisting of the constructed clusters. But, it is inadequate to use the clustering technique before inferring a network. Instead, several researchers have proposed the methods that execute the gene clustering and the network inference simultaneously. As these methods use a linear model to describe networks, however, they are unsuitable to analyze time-series of gene expression data. In order to overcome the drawbacks of the existing approaches, this study proposes a new method that executes the gene clustering and the network inference simultaneously. As the proposed method uses a set of non-linear differential equations to describe networks, it has an ability to analyze time-series of gene expression data. As the clustering algorithm, we use the robust EM curve clustering algorithm proposed by Chamroukhi. Through numerical experiments, we finally show the effectiveness of the proposed method.

A number of genetic network inference methods have been proposed. These methods often infer many erroneous regulations. In order to decrease the number of erroneous regulations, this study uses a priori knowledge that biochemical networks exhibit hierarchical structures. This study detects the hierarchical structure in the target network using a hierarchical random graph model proposed by Clauset and colleagues. When the regulations inferred by the inference method are inconsistent with the detected hierarchical structure, we can conclude that they are unreasonable. However, it is not always easy to detect the hierarchical structure in the target network because of the regulations erroneously inferred by the inference method. In order to obtain a reasonable hierarchical structure, this study first infers a large number of genetic networks from the observed gene expression data by using a method that combines a genetic network inference method with a bootstrap method. We then extract a hierarchical structure from the inferred multiple genetic networks so that it is consistent with most of the networks. Through numerical experiments, we finally show that the use of the hierarchical structure in the network improves the reliabilities of regulations inferred by the genetic network inference method.

Vohradský has proposed a neural network model to describe biochemical networks. Based on this model, several researchers have proposed genetic network inference methods. When trying to analyze large-scale genetic networks, however, these methods must solve high-dimensional function optimization problems. In order to resolve the high-dimensionality in the estimation of the parameters of the Vohradský's neural network model, this study proposes a new method. The proposed method estimates the parameters of the neural network model by solving two-dimensional function optimization problems. Although these two-dimensional problems are non-linear, their low-dimensionality would make the estimation of the model parameters easier. Finally, we confirm the effectiveness of the proposed method through numerical experiments.

In order to reduce coupling and increase cohesion, we refactor program source code. Previous research efforts for suggesting candidates of such refactorings are based on static analysis, which obtains relations among classes or methods from source code. However, these approaches cannot obtain runtime information such as repetition count of loop, dynamic dispatch and actual execution path. Therefore, previous approaches might miss some refactoring opportunities. To tackle this problem, we propose a technique to find refactoring candidates by analyzing method traces. We have implemented a prototype tool based on the proposed technique and evaluated the technique on two software systems. As a result, we confirmed that the proposed technique could detect some refactoring candidates, which increase code quality.

For the inference of S-system models of genetic networks, this study proposes a new method, i.e., a two-phase estimation method. The two-phase estimation method is an extension of the decoupling approach proposed by Voit and Almeida. The decoupling approach defines the estimation of S-system parameters as a problem of solving sets of non-linear algebraic equations. Our method first transforms each set of non-linear algebraic equations, that is defined by the decoupling approach, into a set of linear ones. The transformation of the equations is easily accomplished by solving a linear programming problem. The proposed method then estimates S-system parameters by solving the transformed linear equations. As the proposed two-phase estimation method infers an S-system model only by solving linear programming problems and sets of linear algebraic equations, it always provides us with a unique solution. Moreover, its computational cost is very low. Finally, we confirm the effectiveness of the proposed method through numerical experiments.

Practical function optimization problems often con tain several constraints. Although evolutionary algorithms (EAs) have been successfully applied to unconstrained real-parameter optimization problems, it is sometimes difficult for these methods even to And feasible solutions in constrained ones. In this study, we thus propose a technique that makes EAs possible to solve function optimization problems with several inequality and a single equality constraints. The proposed technique simply forces individuals newly generated to satisfy the equality constraint. In order to generate these individuals, this study utilizes a Markov chain Monte Carlo (MCMC) method and crossover kernels. While the proposed technique can be applied to any EA, this study applies it to a relatively simple one, UNDX/MGG. Experimental results show that UNDX/MGG with the proposed technique has an ability to solve unimodal and multimodal function optimization problems with constraints. Finally, we show that, although our approach cannot solve function optimization problems with multiple equality constraints, we can convert some of them into those with a single equality constraint.

An S-system model is considered as an ideal model for describing genetic networks. As one of effective techniques for inferring S-system models of genetic networks, the problem decomposition strategy has been proposed. This strategy defines the inference of a genetic network consisting of N genes as N subproblems, each of which is a 2(N+1)-dimensional function optimization problem. When we try to infer large-scale genetic networks consisting of many genes, however, it is not always easy for function optimization algorithms to solve 2(N + 1)-dimensional problems. In this study, we thus propose a new technique that transforms the 2(N + 1)-dimensional S-system parameter estimation problems into (N+2)-dimensional problems. The proposed technique reduces the search dimensions of the problems by solving linear programming problems. The transformed problems are then optimized using evolutionary algorithms. Finally, through numerical experiments on an artificial genetic network inference problem, we show that the proposed dimension reduction approach is more than 3 times faster than the problem decomposition approach.

MOTIVATION: Clustering and gene network inference often help to predict the biological functions of gene subsets. Recently, researchers have accumulated a large amount of time-course transcriptome data collected under different treatment conditions to understand the physiological states of cells in response to extracellular stimuli and to identify drug-responsive genes. Although a variety of statistical methods for clustering and inferring gene networks from expression profiles have been proposed, most of these are not tailored to simultaneously treat expression data collected under multiple stimulation conditions. RESULTS: We propose a new statistical method for analyzing temporal profiles under multiple experimental conditions. Our method simultaneously performs clustering of temporal expression profiles and inference of regulatory relationships among gene clusters. We applied this method to MCF7 human breast cancer cells treated with epidermal growth factor and heregulin which induce cellular proliferation and differentiation, respectively. The results showed that the method is useful for extracting biologically relevant information. AVAILABILITY: A MATLAB implementation of the method is available from http://csb.gsc.riken.jp/yshira/software/clusterNetwork.zip.

Recently, the inference of genetic networks was defined as a series of discrimination tasks. The inference method based on this problem definition infers genetic networks by obtaining predictors that can predict the signs of the differential coefficients of the gene expression levels. As these predictors are obtained by solving linear programming problems, the computational time of the method is very short. The method however has no explicit mechanism to utilize a priori knowledge about genetic networks. This study therefore extends the inference method based on the discrimination tasks to make it possible to utilize the a priori knowledge. In order to verify its effectiveness, we then apply the modified method to artificial genetic network inference problems.

MOTIVATION: Genetic network inference methods based on sets of differential equations generally require a great deal of time, as the equations must be solved many times. To reduce the computational cost, researchers have proposed other methods for inferring genetic networks by solving sets of differential equations only a few times, or even without solving them at all. When we try to obtain reasonable network models using these methods, however, we must estimate the time derivatives of the gene expression levels with great precision. In this study, we propose a new method to overcome the drawbacks of inference methods based on sets of differential equations. RESULTS: Our method infers genetic networks by obtaining classifiers capable of predicting the signs of the derivatives of the gene expression levels. For this purpose, we defined a genetic network inference problem as a series of discrimination tasks, then solved the defined series of discrimination tasks with a linear programming machine. Our experimental results demonstrated that the proposed method is capable of correctly inferring genetic networks, and doing so more than 500 times faster than the other inference methods based on sets of differential equations. Next, we applied our method to actual expression data of the bacterial SOS DNA repair system. And finally, we demonstrated that our approach relates to the inference method based on the S-system model. Though our method provides no estimation of the kinetic parameters, it should be useful for researchers interested only in the network structure of a target system. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Sakuma and Kobayashi have proposed a density estimation method that utilizes real-coded crossover operators. However, their method was used only to estimate normal distribution functions. In order to estimate more complicated PDFs, this study proposes a new density estimation method of utilizing crossover operators. When we try to solve function optimization problems, on the other hand, real-coded genetic algorithms (GAs) show good performances if their crossover operators have an ability to estimate the PDF of the population well. Thus, this study then applies our density estimation method into a simple real-coded GA to improve its search performance. Finally, through numerical experiments, we verify the effectiveness of the proposed density estimation method.

BACKGROUND: The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks. RESULTS: Through numerical experiments on artificial genetic network inference problems, we demonstrated that our method has the ability to infer genetic networks correctly and it was faster than the other inference methods. We then applied the proposed method to actual expression data of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. When our method inferred the genetic network from the actual data, it required about 4.7 min on a single-CPU personal computer. CONCLUSION: The proposed method has an ability to obtain reasonable networks with a short computational time. As a high performance computer is not always available at every laboratory, the short computational time of our method is a preferable feature. There does not seem to be a perfect model for the inference of genetic networks yet. Therefore, in order to extract reliable information from the observed gene expression data, we should infer genetic networks using multiple inference methods based on different models. Our approach could be used as one of the promising inference methods.

The inference of genetic networks using a model based on a set of differential equations is generally time-consuming. In order to decrease its computational time, we have proposed the inference method using a normalized Gaussian network (NGnet) model. The inferred models however contain many false-positive regulations when we apply the NGnet approach to the genetic network inference problems. This paper proposes the reduced NGnet model and the gradual reduction strategy to overcome the drawbacks of the NGnet approach. Then, in order to verify their effectiveness, we apply the inference method using the proposed techniques to several artificial genetic network inference problems.

A model based on a set of differential equations can effectively capture various dynamics. This type of model is, therefore, ideal for describing genetic networks. The genetic network inference problem based on a set of differential equations is generally defined as a parameter estimation problem. On the basis of this problem definition, several computational methods have been proposed so far. On the other hand, the genetic network inference problem based on a set of differential equations can be also defined as a function approximation problem. For solving the defined function approximation problem, any type of function approximator is available. In this study, on the basis of the latter problem definition, we propose a new method for the inference of genetic networks using a normalized Gaussian network model. As the EM algorithm is available for the learning of the NGnet model, the computational time of the proposed method is much shorter than those of other inference methods. The effectiveness of the proposed inference method is verified through numerical experiments of several artificial genetic network inference problems.

We propose a new method for the inference of the genetic networks. The proposed method uses a neural network model to describe the genetic network. The inference of the neural network model of the genetic network is defined as the function optimization problem. As the function optimizer for this problem, a genetic local search is used. At this time, to enhance the probability of finding a reasonable solution, we introduce a priori knowledge about the genetic network into the objective function. In this paper, we also propose the method based on the sensitivity analysis to interpret the optimized neural network model. Through artificial genetic network inference problems, we verify the effectiveness of the proposed method.

The random number generator is one of the important components of evolutionary algorithms (EAs). Therefore, when we try to solve function optimization problems using EAs, we must carefully choose a good pseudo-random number generator. In EAs, the pseudo-random number generator is often used for creating uniformly distributed individuals. As the low-discrepancy sequences allow us to create individuals more uniformly than the random number sequences, we apply the low-discrepancy sequence generator, instead of the pseudo-random number generator, to EAs in this study. The numerical experiments show that the low-discrepancy sequence generator improves the search performances of EAs.

MOTIVATION: To resolve the high-dimensionality of the genetic network inference problem in the S-system model, a problem decomposition strategy has been proposed. While this strategy certainly shows promise, it cannot provide a model readily applicable to the computational simulation of the genetic network when the given time-series data contain measurement noise. This is a significant limitation of the problem decomposition, given that our analysis and understanding of the genetic network depend on the computational simulation. RESULTS: We propose a new method for inferring S-system models of large-scale genetic networks. The proposed method is based on the problem decomposition strategy and a cooperative coevolutionary algorithm. As the subproblems divided by the problem decomposition strategy are solved simultaneously using the cooperative coevolutionary algorithm, the proposed method can be used to infer any S-system model ready for computational simulation. To verify the effectiveness of the proposed method, we apply it to two artificial genetic network inference problems. Finally, the proposed method is used to analyze the actual DNA microarray data.

UNLABELLED: OBIYagns (yet another gene network simulator) is a biochemical system simulator that comprises a multiple-user Web-based graphical interface, an ordinary differential equation solver and a parameter estimators distributed over an open bioinformatics grid (OBIGrid). This grid-based biochemical simulation system can achieve high performance and provide a secure simulation environment for estimating kinetic parameters in an acceptable time period. OBIYagns can be applied to larger system biology-oriented simulation projects. AVAILABILITY: OBIYagns example models, methods and user guide are available at https://access.obigrid.org/yagns/ SUPPLEMENTARY INFORMATION: Please refer to Bioinformatics online.

In this paper, we propose a new method for the inference of S-system models of large-scale genetic networks. This method employs a technique to decompose the genetic network inference problem into several subproblems, and then applies a genetic local search to each of the subproblems. A local search method utilizing the feature of the S-system model is used as one of the search operators in this genetic local search. Finally, the effectiveness of the proposed method is verified through a genetic network inference problem.

In this paper, we propose a new genetic local search named GLSDC (a genetic local search with distance independent diversity control) by extending the basic idea of DIDC (a genetic algorithm with distance independent diversity control) to coarse grained parallelization. GLSDC employs a local search method as a search operator. GLSDC also uses genetic operators, i.e., a crossover operator and a generation alternation model. However, in GLSDC, the crossover operator is not used as a search operator, but is used only for converging the population. GLSDC has an ability to find multiple optima simultaneously by stacking good individuals that have been found by the local search. Finding multiple optima is often required when we try to solve real world problems. The effectiveness of the proposed method is verified through numerical experiments on several high dimensional benchmark problems.