Different types of Bernstein operators in inference of Gaussian graphical model

• Main Authors: Melih Ağraz, Vilda Purutçuoğlu
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: Gaussian graphical model; Bernstein operators; Bleiman Butzer Hahn operators; Meyer-König and Zeller operators; systems biology; bioinformatics; statistics
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1154706

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-König, 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.