Extended lasso-type MARS (LMARS) model in the description of biological network

Ağraz, Melih; Purutçuoğlu, Vi̇lda

doi:10.1080/00949655.2018.1531414

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…These genes are also selected as the core genes in the literature of gynaecological cancer and the quasi true network structure of these genes is represented by a complete graph meaning that all the entries of the adjacency matrix are composed of ones [6]. By using the algorithm described in the study of [8] and explained in Section 2.2.2 under the application of the C-vine approach, the order of the variables is estimated as (4,6,5,7,8,2,10,9,1,3) and the computed C-vine copulas are listed in Table 5. In this analyses, we apply the VineCopula package in R [7].…”

Section: Datamentioning

confidence: 99%

“…But, in the literature of the construction of biological networks, there exists different types of non-parametric models as well. One of the recent methods is called the loop-based multivariate adaptive regression splines (LMARS) [1,4] and its conic version [5]. These two models adapt the multivariate adap-precision matrix, shows the conditional dependence in such a way that each zero element of the precision matrix implies the conditionally independence between corresponding variables.…”

Section: Introductionmentioning

confidence: 99%

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Vine copula graphical models in the construction of biological networks

Farnoudkia¹,

Purutçuoğlu²

2021

Hacettepe Journal of Mathematics and Statistics

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The copula Gaussian graphical model (CGGM) is one of the major mathematical models for high dimensional biological networks which provides a graphical representation, especially, for sparse networks. Basically, this model uses a regression of the Gaussian graphical model (GGM) whose precision matrix describes the conditional dependence between the variables to estimate the coefficients of the linear regression model. The Bayesian inference for the model parameters is used to overcome the dimensional limitation of GGM under sparse networks and small sample sizes. But from the application in bench-mark data sets, it is seen that although CGGM is successful in certain systems, it may not fit well for non-normal multivariate observations. In this study, we propose the vine copulas to relax the strict normality assumption of CGGM and to describe networks from a variety of copulas alternates besides the Gaussian copula. Accordingly, we evaluate the best fitted bivariate copula distribution for every pairwise gene and compute the estimated adjacency matrix which denotes the presence of an edge between the corresponding genes. We assess the performance of our proposed approach in three network data via distinct accuracy measures by comparing the outputs with the results of the CGGM.

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