Yoon-Sung Jung

A copula method for modeling directional dependence of genes

BackgroundGenes interact with each other as basic building blocks of life, forming a complicated network. The relationship between groups of genes with different functions can be represented as gene networks. With the deposition of huge microarray data sets in public domains, study on gene networking is now possible. In recent years, there has been an increasing interest in the reconstruction of gene networks from gene expression data. Recent work includes linear models, Boolean network models, and Bayesian networks. Among them, Bayesian networks seem to be the most effective in constructing gene networks. A major problem with the Bayesian network approach is the excessive computational time. This problem is due to the interactive feature of the method that requires large search space. Since fitting a model by using the copulas does not require iterations, elicitation of the priors, and complicated calculations of posterior distributions, the need for reference to extensive search spaces can be eliminated leading to manageable computational affords. Bayesian network approach produces a discretely expression of conditional probabilities. Discreteness of the characteristics is not required in the copula approach which involves use of uniform representation of the continuous random variables. Our method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation.ResultsWe analyzed the gene interactions for two gene data sets (one group is eight histone genes and the other group is 19 genes which include DNA polymerases, DNA helicase, type B cyclin genes, DNA primases, radiation sensitive genes, repaire related genes, replication protein A encoding gene, DNA replication initiation factor, securin gene, nucleosome assembly factor, and a subunit of the cohesin complex) by adopting a measure of directional dependence based on a copula function. We have compared our results with those from other methods in the literature. Although microarray results show a transcriptional co-regulation pattern and do not imply that the gene products are physically interactive, this tight genetic connection may suggest that each gene product has either direct or indirect connections between the other gene products. Indeed, recent comprehensive analysis of a protein interaction map revealed that those histone genes are physically connected with each other, supporting the results obtained by our method.ConclusionThe results illustrate that our method can be an alternative to Bayesian networks in modeling gene interactions. One advantage of our approach is that dependence between genes is not assumed to be linear. Another advantage is that our approach can detect directional dependence. We expect that our study may help to design artificial drug candidates, which can block or activate biologically meaningful pathways. Moreover, our copula approach can be extended to investigate the effects of local environments on protein-protein interactions. The copula mutual information approach will help to propose the new variant of ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks): an algorithm for the reconstruction of gene regulatory networks.

Mixture of D-vine copulas for modeling dependence

The identification of an appropriate multivariate copula for capturing the dependence structure in multivariate data is not straightforward. The reason is because standard multivariate copulas (such as the multivariate Gaussian, Student-t, and exchangeable Archimedean copulas) lack flexibility to model dependence and have other limitations, such as parameter restrictions. To overcome these problems, vine copulas have been developed and applied to many applications. In order to reveal and fully understand the complex and hidden dependence patterns in multivariate data, a mixture of D-vine copulas is proposed incorporating D-vine copulas into a finite mixture model. As a D-vine copula has multiple parameters capturing the dependence through iterative construction of pair-copulas, the proposed model can facilitate a comprehensive study of complex and hidden dependence patterns in multivariate data. The proposed mixture of D-vine copulas is applied to simulated and real data to illustrate its performance and benefits.

Partial correlation with copula modeling

We propose a new partial correlation approach using Gaussian copula. Our empirical study found that the Gaussian copula partial correlation has the same value as that which is obtained by performing a Pearsons partial correlation. With the proposed method, based on canonical vine and d-vine, we captured direct interactions among eight histone genes.

New Approach of Directional Dependence in Exchange Markets Using Generalized FGM Copula Function

This article presents an application of copula methodology in exchange markets. In this article, we consider the concept of directional dependence given by Sungur (2005). We also consider and study directional dependence for generalized Farlie–Gumbel–Morgenstern (FGM) distributions, which are a member of the Rodríguez-Lallena and Úbeda-Flores (2004) family, C(u, v) = uv + f(u)g(v). Examples of the generalized FGM distributions are provided with exchange market data of the Euro, Canadian dollar, Korean Won, Japanese Yen, and Hong Kong dollar against the U.S. dollar.

Large asymmetry and directional dependence by using copula modeling to currency exchange rates

To examine the asymmetry of financial data in detail, we have considered both the tail dependence with diverse copulas and Jung et al.s (8) directional dependence by copula. From the empirical study in this paper, we have found that the tail dependence by Pattons (11) modified symmetrized Joe-Clayton copula function did not show the asymmetry property sufficiently because there is no tail dependence for the currency exchange rates of Republic of Korea and Japan against the US dollar after the 2008 financial crisis. However, by using the copula approach for directional dependence, we showed that there exists the asymmetry of the currency exchange rates of Republic of Korea and Japan against the US dollar before and after the 2008 financial crisis because the directional dependence only when existing an asymmetry of data can be found. We conclude that the copula approach for directional dependence can be supplemented to explain the asymmetry property in addition to the tail dependence approach.

Directional Dependence of Genes Using Survival Truncated FGM Type Modification Copulas

A multivariate distribution can be represented in terms of its underlying margins by binding these margins together using a copula function (Sklar, 1959). Here, we propose a new class of survival FGM-type modification truncated copulas which quantify dependency and incorporate directional dependence. In addition, we apply our proposed methods to the analysis of directional dependence relationships between genes. Finally, we employ the Akaike Information Criterion (AIC) to check the goodness of fit for our proposed copula models.

Truncation invariant copulas for modeling directional dependence: Application to foreign currency exchange data

Directional dependence modeling has been applied to many research areas including economics, finance, biostatistics, and bioinformatics. The concept of directional dependence using copula regression functions has been introduced by Sungur [21]. So we propose a new copula family which incorporates the truncation invariant structure [20] into the generalized Farlie-Gumbel-Morgenstern (FGM) distributions. The directional dependence of the new truncated invariant FGM copulas will be also introduced in this research. We will show that there exists a directional dependence in our truncation invariant FGM copulas using Foreign Currency Exchange Data of the Canadian Dollar (CAD/USD), the Japanese Yen (JPY/USD), and the Korean Won (KRW/USD).