Different types of Bernstein operators in inference of Gaussian graphical model

Download

10.1080:23311835.2016.1154706.pdf

Date

2016-01-01

Author

Agraz, Melih
Purutçuoğlu Gazi, Vilda

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

95
views

83
downloads

The Gaussian graphical model (GGM) is a powerful tool to describe the relationship between the nodes via the inverse of the covariance matrix in a complex biological system. But the inference of this matrix is problematic because of its high dimension and sparsity. From previous analyses, it has been shown that the Bernstein and Szasz polynomials can improve the accuracy of the estimate if they are used in advance of the inference as a processing step of the data. Hereby in this study, we consider whether any type of the Bernstein operators such as the Bleiman Butzer Hahn, Meyer-Konig, and Zeller operators can be performed for the improvement of the accuracy or only the Bernstein and the Szasz polynomials can satisfy this condition. From the findings of the Monte Carlo runs, we detect that the highest accuracies in GGM can be obtained under the Bernstein and Szasz polynomials, rather than all other types of the Bernstein polynomials, from small to high-dimensional biological networks.

Subject Keywords

Gaussian graphical model, Bernstein operators, Bleiman Butzer Hahn operators, Meyer-Konig and Zeller operators, Systems biology, Bioinformatics, Statistics

URI

https://hdl.handle.net/11511/35379

Journal

COGENT MATHEMATICS

DOI

https://doi.org/10.1080/23311835.2016.1154706

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Different types of modellings and the inference of model parameters for complex biological systems Ağraz, Melih; Purutçuoğlu Gazi, Vilda; Department of Statistics (2017) A reaction set that form a system can be modeled mathematically in different ways such as boolean, ordinary differential equations and stochastic modellings. Among them the random system is merely taken into account by the stochastic approach that is based on the known number of molecules in the reactions and if we consider the behaviour of the system under steady state condition, the modelling can be done via deterministic methods such as the ordinary differential equation. In this thesis, firstly, we aim ...
Novel model selection criteria on high dimensionalbiological networks Bülbül, Gül Baha; Purutçuoğlu Gazi, Vilda; Department of Statistics (2019) Gaussian graphical model (GGM) is an useful tool to describe the undirected associ-ations among the genes in the sparse biological network. To infer such high dimen-sional biological networks, thel1-penalized maximum-likelihood estimation methodis used. This approach performs a variable selection procedure by using a regular-ization parameter which controls the sparsity in the network. Thus, a selection ofthe regularization parameter becomes crucial to define the true interactions in the bi-ological ne...
Comparison of two inference approaches in Gaussian graphical models Purutçuoğlu Gazi, Vilda; Wit, Ernst (Walter de Gruyter GmbH, 2017-04-01) Introduction: The Gaussian Graphical Model (GGM) is one of the well-known probabilistic models which is based on the conditional independency of nodes in the biological system. Here, we compare the estimates of the GGM parameters by the graphical lasso (glasso) method and the threshold gradient descent (TGD) algorithm.
NON-EUCLIDEAN VECTOR PRODUCT FOR NEURAL NETWORKS Afrasiyabi, Arman; Badawi, Diaa; Nasır, Barış; Yildiz, Ozan; Yarman Vural, Fatoş Tunay; ÇETİN, AHMET ENİS (2018-04-20) We present a non-Euclidean vector product for artificial neural networks. The vector product operator does not require any multiplications while providing correlation information between two vectors. Ordinary neurons require inner product of two vectors. We propose a class of neural networks with the universal approximation property over the space of Lebesgue integrable functions based on the proposed non-Euclidean vector product. In this new network, the "product" of two real numbers is defined as the sum ...
Novel model selection criteria for LMARS: MARS designed for biological networks Bulbul, Gul Bahar; Purutçuoğlu Gazi, Vilda (2021-03-01) In higher dimensions, the loop-based multivariate adaptive regression splines (LMARS) model is used to build sparse and complex gene structure nonparametrically by correctly defining its interactions in the network. Also, it prefers to apply the generalized cross-validation (GCV) value as its original model selection criterion in order to select the best model, in turn, represent the true network structure. In this study, we suggest to modify the model selection procedure of LMARS by changing GCV with our K...

Citation Formats

M. Agraz and V. Purutçuoğlu Gazi, “Different types of Bernstein operators in inference of Gaussian graphical model,” COGENT MATHEMATICS, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35379.