MARS as an alternative approach of Gaussian graphical model for biochemical networks

Ayyildiz, Ezgi; Ağraz, Melih; Purutçuoğlu, Vi̇lda

doi:10.1080/02664763.2016.1266465

Cited by 12 publications

(4 citation statements)

References 42 publications

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“…Our analyses of the MARS (multivariate adaptive regression) approach (Friedman, ) that is based on the spline functions, support this finding. The results show promising accuracies when they are compared with glasso approach of GGM (Ayyıldız, Ağraz, & Purutçuoğlu, ).…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Bernstein approximations in glasso‐based estimation of biological networks

2017

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The Gaussian graphical model (GGM) is one of the common dynamic modelling approaches in the construction of gene networks. In inference of this modelling the interaction between genes can be detected mainly via graphical lasso (glasso) or coordinate descent‐based approaches. Although these methods are successful in moderate networks, their performances in accuracy decrease when the system becomes sparser. We here implement a particular type of polynomial transformations, called the Bernstein polynomials, of the network data in advance of their inference to raise the accuracy. From comparative Monte Carlo studies and real data analyses we show that these polynomials are successful in terms of the precision, specificity and F‐measure when the scale‐free networks are modelled via GGM and estimated by glasso, and accordingly they can be used as a preprocessing step in inference of these networks. The Canadian Journal of Statistics 45: 62–76; 2017 © 2017 Statistical Society of Canada

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Section: Conclusion and Discussionmentioning

confidence: 96%

Bernstein approximations in glasso‐based estimation of biological networks

2017

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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%

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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“…MARS bunlara örnek olarak verilebilir. 16,17 Parametrik model alternatifleri içinde ise en öne çıkanları Kopula GGM modelidir. 18,19 Bu model, kısaca, GGM ifadesindeki çok değişkenli normal dağılım fonksiyonunun, Gaussian kopula yardı-mıyla yazılmasından türetilmiştir.…”

Section: İleri̇ Modellerunclassified

Mathematical Modeling of Gene Networks: Review

Purutçuoğlu¹,

Ayyildiz²

2017

Turkiye Klinikleri J Biostat

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ÖZET Sistem ve hesaplamalı biyoloji alanları, deneysel teknolojinin ilerlemesiyle gelişen ve biyolojik/kimyasal sistem olaylarının anlaşılmasını sağlayacak matematiksel metotları ve modelleri kapsamaktadır. Bu modeller sistem elemanlarının davranışlarının daha iyi anlaşılmasına ve gerektiğinde, bu sistemlerin simülasyonlar yardımıyla yaratılmasına ve birbirleriyle karşılaştırılmasına yardımcı olmaktadır. Ayrıca, matematiksel modellemeler, sistem hakkındaki mevcut bilgilerin doğruluğunun da test edilmesine ve laboratuvar ortamında yapılması maliyetli olabilecek deneyleri yorumlayabilmemize olanak sağlamaktadır. Bu çalışmada, farklı varsayımlara ve veri çeşitle-rine göre karmaşık gen ağlarının nasıl modellenebileceği matematiksel ifadelerle açıklanacak ve önerilen alternatif modellerden çıkabilecek ağlar, grafiksel şekillerle anlatılacaktır. Burada sunulan temel yaklaşımların gerçek veri setleri üzerinde uygulanması durumunda, sistemlerden biyolojik olarak önemli olabilecek sonuçların elde edilmesinin mümkün olabileceği düşünülmektedir. Ayrıca, tanıtılan bu modellerin sadece gen ağlarında değil, yüksek boyutlu başka veri analizlerinde de kullanılması mümkündür. Nitekim sistem biyolojinin alt dallarından olan sistem modellemesi ve gen ağlarının modellenmesi, temelde, yüksek boyutlu ve çok değişkenli verilerin analizine imkan veren, karmaşık modellemeler üzerine yoğunlaşmıştır, ve bu çalışma da bunun bir ör-neğidir.Anahtar Kelimeler: Gen düzenleyici şebekeler; modeller, teorik; sistem biyolojisi; sistem modellemesi; gen ağlarının modellenmesi ABSTRACT System and computational biology areas cover mathematical methods and models that improve with the advancement of experimental technology and enable us to understand biological/chemical systems. These models help to better understand the behaviors of system components, and when necessary, can be able to generate and compare these systems via simulations. Furthermore, mathematical models can be able to validate the current knowledge about the systems and enables us to interpret the experiments that can be expensive to perform in the wet-lab. In this study, we explain how complex gene networks can be modelled by using mathematical expressions under various data types and assumptions, and the networks which are constructed by the suggested alternative models are represented by graphical figures. It is expected to obtain biologically valuable findings from these underlying systems when these fundamental approaches presented here are applied to real data set. Moreover, it is possible to implement these models not only in the field of gene networks, but also, in the application of other high dimensional data analyses. As a matter of fact, systems modeling and gene network modeling are the branches of the systems biology and focus on complex models that enable us to model high-dimensional and multivariate data, and this study is an example of this.

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MARS as an alternative approach of Gaussian graphical model for biochemical networks

Cited by 12 publications

References 42 publications

Bernstein approximations in glasso‐based estimation of biological networks

Bernstein approximations in glasso‐based estimation of biological networks

Vine copula graphical models in the construction of biological networks

Mathematical Modeling of Gene Networks: Review

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