Search

Abstract: This paper considers a class of feature selecting support vector machines (SVMs) based on -norm regularization, where . The standard SVM [Vapnik, V., 1995. The Nature of Statistical Learning Theory. Springer, NY.] minimizes the hinge loss function subject to the -norm penalty. Recently, -norm SVM ( -SVM) [Bradley, P., Mangasarian, O., 1998. Feature selection via concave minimization and support vector machines. In: Machine Learning Proceedings of the Fifteenth International Conference (ICML98). Citeseer, pp. 82–90.] was suggested for feature selection and has gained great popularity since its introduction. -norm penalization would result in more powerful sparsification, but exact solution is NP-hard. This raises the question of whether fractional-norm ( for between 0 and 1) penalization can yield benefits over the existing , and approximated approaches for SVMs. The major obstacle to answering this is that the resulting objective functions are non-convex. This paper addresses the difficult optimization problems of fractional-norm SVM by introducing a new algorithm based on the Difference of Convex functions (DC) programming techniques [Pham Dinh, T., Le Thi, H., 1998. A DC optimization algorithm for solving the trust-region subproblem. SIAM J. Optim. 8 (2), 476–505. Le Thi, H., Pham Dinh, T., 2008. A continuous approach for the concave cost supply problem via DC programming and DCA. Discrete Appl. Math. 156 (3), 325–338.], which efficiently solves a reweighted -SVM problem at each iteration. Numerical results on seven real world biomedical datasets support the effectiveness of the proposed approach compared to other commonly-used sparse SVM methods, including -SVM, and recent approximated -SVM approaches. [Copyright &y& Elsevier]

Abstract: In this paper, we consider how to recover the structure of a Bayesian network from a moral graph. We present a more accurate characterization of moral edges, based on which a complete subset (i.e., a separator) contained in the neighbor set of one vertex of the putative moral edge in some prime block of the moral graph can be chosen. This results in a set of separators needing to be searched generally smaller than the sets required by some existing algorithms. A so-called structure-finder algorithm is proposed for structural learning. The complexity analysis of the proposed algorithm is discussed and compared with those for several existing algorithms. We also demonstrate how to construct the moral graph locally from, separately, the Markov blanket, domain knowledge and -separation trees. Simulation studies are used to evaluate the performances of various strategies for structural learning. We also analyze a gene expression data set by using the structure-finder algorithm. [Copyright &y& Elsevier]

Abstract: In cancer classification based on gene expression data, it would be desirable to defer a decision for observations that are difficult to classify. For instance, an observation for which the conditional probability of being cancer is around 1/2 would preferably require more advanced tests rather than an immediate decision. This motivates the use of a classifier with a reject option that reports a warning in cases of observations that are difficult to classify. In this paper, we consider a problem of gene selection with a reject option. Typically, gene expression data comprise of expression levels of several thousands of candidate genes. In such cases, an effective gene selection procedure is necessary to provide a better understanding of the underlying biological system that generates data and to improve prediction performance. We propose a machine learning approach in which we apply the penalty to the SVM with a reject option. This method is referred to as the SVM with a reject option. We develop a novel optimization algorithm for this SVM, which is sufficiently fast and stable to analyze gene expression data. The proposed algorithm realizes an entire solution path with respect to the regularization parameter. Results of numerical studies show that, in comparison with the standard SVM, the proposed method efficiently reduces prediction errors without hampering gene selectivity. [Copyright &y& Elsevier]

Abstract: It is well known that the boosting-like algorithms, such as AdaBoost and many of its modifications, may over-fit the training data when the number of boosting iterations becomes large. Therefore, how to stop a boosting algorithm at an appropriate iteration time is a longstanding problem for the past decade (see ). applied model selection criteria to estimate the stopping iteration for Boosting, but it is still necessary to compute all boosting iterations under consideration for the training data. Thus, the main purpose of this paper is focused on studying the early stopping rule for Boosting during the training stage to seek a very substantial computational saving. The proposed method is based on a change point detection method on the values of model selection criteria during the training stage. This method is also extended to two-class classification problems which are very common in medical and bioinformatics applications. A simulation study and a real data example to these approaches are provided for illustrations, and comparisons are made with LogitBoost. [Copyright &y& Elsevier]

The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world applications, it is important to develop algorithms to solve the lasso that efficiently scale up to problems of this size. Discarding features from certain steps of the algorithm is a powerful technique for increasing efficiency and addressing the Big Data challenge. This paper proposes a family of hybrid safe–strong rules (HSSR) which incorporate safe screening rules into the sequential strong rule (SSR) to remove unnecessary computational burden. Two instances of HSSR are presented, SSR-Dome and SSR-BEDPP, for the standard lasso problem. SSR-BEDPP is further extended to the elastic net and group lasso problems to demonstrate the generalizability of the hybrid screening idea. Extensive numerical experiments with synthetic and real data sets are conducted for both the standard lasso and the group lasso problems. Results show that the proposed hybrid rules can substantially outperform existing state-of-the-art rules. [ABSTRACT FROM AUTHOR]