Related papers: Feature selection in linear SVMs via a hard cardin…

Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the…

Support vector machines (SVMs) are widely used and constitute one of the best examined and used machine learning models for two-class classification. Classification in SVM is based on a score procedure, yielding a deterministic…

Support Vector Machine (SVM) is a state-of-the-art classification method widely used in science and engineering due to its high accuracy, its ability to deal with high dimensional data, and its flexibility in modeling diverse sources of…

Economic models produce moment inequalities, which can be used to form tests of the true parameters. Confidence sets (CS) of the true parameters are derived by inverting these tests. However, they often lack analytical expressions,…

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, where the positive partial transpose…

We present a new wrapper feature selection algorithm for human detection. This algorithm is a hybrid feature selection approach combining the benefits of filter and wrapper methods. It allows the selection of an optimal feature vector that…

Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out…

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel…

We extend rank-constrained optimization to general hyperbolic programs (HP) using the notion of matroid rank. For LP and SDP respectively, this reduces to sparsity-constrained LP and rank-constrained SDP that are already well-studied. But…

Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve…

Feature selection is important step in machine learning since it has shown to improve prediction accuracy while depressing the curse of dimensionality of high dimensional data. The neural networks have experienced tremendous success in…

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…

Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regression matrix to effectively capture the intrinsic structure…

In this paper, we consider the binary classification problem via distributed Support-Vector-Machines (SVM), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global…

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…

Accurately delineating the visual pathway (VP) is crucial for understanding the human visual system and diagnosing related disorders. Exploring multi-parametric MR imaging data has been identified as an important way to delineate VP.…

Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…