Novel model selection criteria for LMARS: MARS designed for biological networks

Bulbul, Gul Bahar
Purutçuoğlu Gazi, Vilda
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 Kullback-Leibler information-based criteria, namely, consistent Akaike information criterion (CAIC), CAIC with Fisher information matrix and information complexity. Thereby, we aim to compare the performance of our proposal model selection criteria together with the state-of-art model selection criteria, namely, AIC and Bayesian information criterion by comparing their accuracy with GCV while modelling different dimensional and topological biological networks under both simulated and real datasets.


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...
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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.
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Ayyıldız Demirci, Ezgi; Purutçuoğlu Gazi, Vilda; Weber, Gerhard Wilhelm (2018-11-01)
The Gaussian Graphical Model (GGM) and its Bayesian alternative, called, the Gaussian copula graphical model (GCGM) are two widely used approaches to construct the undirected networks of biological systems. They define the interactions between species by using the conditional dependencies of the multivariate normality assumption. However, when the system's dimension is high, the performance of the model becomes computationally demanding, and, particularly, the accuracy of GGM decreases when the observations...
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Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an as...
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In this paper we present a Walsh spectrum based method derived from the genetic hill climbing algorithm to improve the non-linearity of functions belonging to Carlet-Feng infinite class of Boolean functions, without degrading other cryptographic properties they possess. We implement our modified algorithms to verify the results and also present a comparison of the resultant cryptographic properties with the original functions.
Citation Formats
G. B. Bulbul and V. Purutçuoğlu Gazi, “Novel model selection criteria for LMARS: MARS designed for biological networks,” JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: