Related papers: Algebraic multigrid support vector machines
Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the…
We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
The transition of the power grid requires new technologies and methodologies, which can only be developed and tested in simulations. Especially larger simulation setups with many levels of detail can become quite slow. Therefore, the number…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
Support vector clustering (SVC) is a versatile clustering technique that is able to identify clusters of arbitrary shapes by exploiting the kernel trick. However, one hurdle that restricts the application of SVC lies in its sensitivity to…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…
We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a "neural computations" point of view into large scale…
Classification is a fundamental task in machine learning. While conventional methods-such as binary, multiclass, and multi-label classification-are effective for simpler problems, they may not adequately address the complexities of some…
We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions…
Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating…
The gradient boosting machine is one of the powerful tools for solving regression problems. In order to cope with its shortcomings, an approach for constructing ensembles of gradient boosting models is proposed. The main idea behind the…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…