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We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression. SNAP is derived from a suitable formulation of the KKT conditions based on Newton derivatives.…
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…
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…
This paper presents a novel framework for designing support vector machines (SVMs), which does not impose restriction on the SVM kernel to be positive-definite and allows the user to define memory constraint in terms of fixed template…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
In this paper we present GSSN, a globalized SCD semismooth* Newton method for solving nonsmooth nonconvex optimization problems. The global convergence properties of the method are ensured by the proximal gradient method, whereas locally…
This paper proposes a frequent pattern data mining algorithm based on support vector machine (SVM), aiming to solve the performance bottleneck of traditional frequent pattern mining algorithms in high-dimensional and sparse data…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
We propose an improved version of the SMO algorithm for training classification and regression SVMs, based on a Conjugate Descent procedure. This new approach only involves a modest increase on the computational cost of each iteration but,…
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…
Convolutional neural networks (CNNs) are similar to "ordinary" neural networks in the sense that they are made up of hidden layers consisting of neurons with "learnable" parameters. These neurons receive inputs, performs a dot product, and…
Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…
We present a novel approach for training kernel Support Vector Machines, establish learning runtime guarantees for our method that are better then those of any other known kernelized SVM optimization approach, and show that our method works…
Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…
Kernelized Support Vector Machines (SVMs) are among the best performing supervised learning methods. But for optimal predictive performance, time-consuming parameter tuning is crucial, which impedes application. To tackle this problem, the…
Kernel methods are used frequently in various applications of machine learning. For large-scale high dimensional applications, the success of kernel methods hinges on the ability to operate certain large dense kernel matrix K. An enormous…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
The Nystr\"om method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or…