Computational Drug Discovery, which uses computational techniques to facilitate and improve the drug discovery process, has aroused considerable interests in recent years. Drug Repositioning (DR) and Drug-Drug Interaction (DDI) prediction are two key problems in drug discovery and many computational techniques have been proposed for them in the last decade. Although these two problems have mostly been researched separately in the past, both DR and DDI can be formulated as the problem of detecting positive interactions between data entities (DR is between drug and disease, and DDI is between pairwise drugs). The challenge in both problems is that we can only observe a very small portion of positive interactions. In this paper, we propose a novel framework called Dyadic Positive-Unlabeled learning (DyPU) to solve the problem of detecting positive interactions. DyPU forces positive data pairs to rank higher than the average score of unlabeled data pairs. Moreover, we also derive the dual formulation of the proposed method with the rectifier scoring function and we show that the associated non-trivial proximal operator admits a closed form solution. Extensive experiments are conducted on real drug data sets and the results show that our method achieves superior performance comparing with the state-of-the-art.

Linear regression is a widely used tool in data mining and machine learning. In many applications, fitting a regression model with only linear effects may not be sufficient for predictive or explanatory purposes. One strategy that has recently received increasing attention in statistics is to include feature interactions to capture the nonlinearity in the regression model. Such model has been applied successfully in many biomedical applications. One major challenge in the use of such model is that the data dimensionality is significantly higher than the original data, resulting in the small sample size large dimension problem. Recently, weak hierarchical Lasso, a sparse interaction regression model, is proposed that produces a sparse and hierarchical structured estimator by exploiting the Lasso penalty and a set of hierarchical constraints. However, the hierarchical constraints make it a non-convex problem and the existing method finds the solution to its convex relaxation, which needs additional conditions to guarantee the hierarchical structure. In this article, we propose to directly solve the non-convex weak hierarchical Lasso by making use of the General Iterative Shrinkage and Thresholding (GIST) optimization framework, which has been shown to be efficient for solving non-convex sparse formulations. The key step in GIST is to compute a sequence of proximal operators. One of our key technical contributions is to show that the proximal operator associated with the non-convex weak hierarchical Lasso admits a closed-form solution. However, a naive approach for solving each subproblem of the proximal operator leads to a quadratic time complexity, which is not desirable for large-size problems. We have conducted extensive experiments on both synthetic and real datasets. Results show that our proposed algorithm is much more efficient and effective than its convex relaxation. To this end, we further develop an efficient algorithm for computing the subproblems with a linearithmic time complexity. In addition, we extend the technique to perform the optimization-based hierarchical testing of pairwise interactions for binary classification problems, which is essentially the proximal operator associated with weak hierarchical Lasso. Simulation studies show that the non-convex hierarchical testing framework outperforms the convex relaxation when a hierarchical structure exists between main effects and interactions.

Linear regression is a widely used tool in data mining and machine learning. In many applications, fitting a regression model with only linear effects may not be sufficient for predictive or explanatory purposes. One strategy which has recently received increasing attention in statistics is to include feature interactions to capture the nonlinearity in the regression model. Such model has been applied successfully in many biomedical applications. One major challenge in the use of such model is that the data dimensionality is significantly higher than the original data, resulting in the small sample size large dimension problem. Recently, weak hierarchical Lasso, a sparse interaction regression model, is proposed that produces sparse and hierarchical structured estimator by exploiting the Lasso penalty and a set of hierarchical constraints. However, the hierarchical constraints make it a non-convex problem and the existing method finds the solution of its convex relaxation, which needs additional conditions to guarantee the hierarchical structure. In this paper, we propose to directly solve the non-convex weak hierarchical Lasso by making use of the GIST (General Iterative Shrinkage and Thresholding) optimization framework which has been shown to be efficient for solving non-convex sparse formulations. The key step in GIST is to compute a sequence of proximal operators. One of our key technical contributions is to show that the proximal operator associated with the non-convex weak hierarchical Lasso admits a closed form solution. However, a naive approach for solving each subproblem of the proximal operator leads to a quadratic time complexity, which is not desirable for large size problems. To this end, we further develop an efficient algorithm for computing the subproblems with a linearithmic time complexity. We have conducted extensive experiments on both synthetic and real data sets. Results show that our proposed algorithm is much more efficient and effective than its convex relaxation.

The patient risk prediction model aims at assessing the risk of a patient in developing a target disease based on his/her health profile. As electronic health records (EHRs) become more prevalent, a large number of features can be constructed in order to characterize patient profiles. This wealth of data provides unprecedented opportunities for data mining researchers to address important biomedical questions. Practical data mining challenges include: How to correctly select and rank those features based on their prediction power? What predictive model performs the best in predicting a target disease using those features? In this paper, we propose top-k stability selection, which generalizes a powerful sparse learning method for feature selection by overcoming its limitation on parameter selection. In particular, our proposed top-k stability selection includes the original stability selection method as a special case given k = 1. Moreover, we show that the top-k stability selection is more robust by utilizing more information from selection probabilities than the original stability selection, and provides stronger theoretical properties. In a large set of real clinical prediction datasets, the top-k stability selection methods outperform many existing feature selection methods including the original stability selection. We also compare three competitive classification methods (SVM, logistic regression and random forest) to demonstrate the effectiveness of selected features by our proposed method in the context of clinical prediction applications. Finally, through several clinical applications on predicting heart failure related symptoms, we show that top-k stability selection can successfully identify important features that are clinically meaningful.