Search

The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the system has many genes and data are far from the normal distribution. Hereby, we construct the model like GGM, but, suggest the long-tailed symmetric distribution (LTS), rather than the normality, and use the modified maximum likelihood (MML) estimator, rather than Glasso, in inference. From the assessment of simulated and real data analyses, it is seen that LTS with MML has higher accuracy and less computational demand with explicit expressions than results of GGM with Glasso. [ABSTRACT FROM AUTHOR]

The multivariate adaptive regression splines (MARS) model is one of the well-known, additive non-parametric models that can deal with highly correlated and nonlinear datasets successfully. From our previous analyses, we have seen that lasso-type MARS (LMARS) can be a strong alternative of the Gaussian graphical model (GGM) which is a well-known probabilistic method to describe the steady-state behaviour of the complex biological systems via the lasso regression. In this study, we extend our original LMARS model by taking into account the second-order interaction effects of genes as the representative of the feed-forward loop in biological networks. By this way, we can describe both linear and nonlinear activations of the genes in the same model. We evaluate the performance of our new model under different dimensional simulated and real systems, and then compare the accuracy of the estimates with GGM and LMARS outputs. The results show the advantage of this new model over its close alternatives. [ABSTRACT FROM AUTHOR]

Objective: Outlier detection is a crucial problem in many fields. Although there are too many outlier detection methods in the literature, only a few methods suitable for dependent, sparse and high dimensional data structure. In this study, we perform various univariate and multivariate outlier detection methods as a pre-processing step before modeling the protein-protein interaction networks in order to investigate whether the outlier detection can improve the accuracy of the model. Material and Methods: Within the univariate approaches, we implement the z-score and Box-plot methods which are the most well-known outlier detection approaches. Besides them, we also apply the multivariate outlier detection methods, called PCOut and Sign which are based on the robust principal component analysis and the BACON method which is a distance-based approach. These methods are applicable for the data type such that the number of variables are bigger than the observation. In the analysis, we use several synthetic and real benchmark biological datasets. Then, we infer the networks with 3 network models, namely, GGM, MARS and CMARS and finally, we check the validity of models via F-measure and the accuracy measures. Conclusion: From the results, it has been seen that the use of outlier detection methods before the modeling cannot contribute to the performance of the models in our datasets. Results: Based on the results obtained from different datasets, we suggest that the estimations of protein-protein interaction networks can be made with GGM, MARS and CMARS methods without the need for an outlier detection process. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]