Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the global optimal solution via an exact optimization method for a problem with dimensions of 1000s may take an impractical amount of CPU time. This suggests the importance of finding suboptimal procedures that can provide good approximate solutions using much less computational effort than exact methods. In this work, we introduce a new procedure and compare it with other popular suboptimal algorithms to solve the best subset selection problem. Extensive computational experiments using synthetic and real data have been performed. The results provide insights into the performance of these methods in different data settings. The new procedure is observed to be a competitive suboptimal algorithm for solving the best subset selection problem for high-dimensional data.

The enormous diversity of life forms thriving in drastically different environmental milieus involves a complex interplay among constituent proteins interacting with each other. However, the organizational principles characterizing the evolution of protein interaction networks (PINs) across the tree of life are largely unknown. Here we study 4,738 PINs belonging to 16 phyla to discover phyla-specific architectural features and examine if there are some evolutionary constraints imposed on the networks' topologies. We utilized positional information of a network's nodes by normalizing the frequencies of automorphism orbits appearing in graphlets of sizes 2-5. We report that orbit usage profiles (OUPs) of networks belonging to the three domains of life are contrastingly different not only at the domain level but also at the scale of phyla. Integrating the information related to protein families, domains, subcellular location, gene ontology, and pathways, our results indicate that wiring patterns of PINs in different phyla are not randomly generated rather they are shaped by evolutionary constraints imposed on them. There exist subtle but substantial variations in the wiring patterns of PINs that enable OUPs to differentiate among different superfamilies. A deep neural network was trained on differentially expressed orbits resulting in a prediction accuracy of 85%.

Neoplasms (NPs) and neurological diseases and disorders (NDDs) are amongst the major classes of diseases underlying deaths of a disproportionate number of people worldwide. To determine if there exist some distinctive features in the local wiring patterns of protein interactions emerging at the onset of a disease belonging to either of these two classes, we examined 112 and 175 protein interaction networks belonging to NPs and NDDs, respectively. Orbit usage profiles (OUPs) for each of these networks were enumerated by investigating the networks' local topology. 56 non-redundant OUPs (nrOUPs) were derived and used as network features for classification between these two disease classes. Four machine learning classifiers, namely, k-nearest neighbour (KNN), support vector machine (SVM), deep neural network (DNN), random forest (RF) were trained on these data. DNN obtained the greatest average AUPRC (0.988) among these classifiers. DNNs developed on node2vec and the proposed nrOUPs embeddings were compared using 5-fold cross validation on the basis of average values of the six of performance measures, viz., AUPRC, Accuracy, Sensitivity, Specificity, Precision and MCC. It was found that nrOUPs based classifier performed better in all of these six performance measures.

This paper presents a variation of Apriori algorithm that includes the role of domain expert to guide and speed up the overall knowledge discovery task. Usually, the user is interested in finding relationships between certain attributes instead of the whole dataset. Moreover, he can help the mining algorithm to select the target database which in turn takes less time to find the desired association rules. Variants of the standard Apriori and Interactive Apriori algorithms have been run on artificial datasets. The results show that incorporating user's preference in selection of target attribute helps to search the association rules efficiently both in terms of space and time.