Related papers: On the convergence of generalized kernel-based int…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…

Video frame interpolation aims at synthesizing intermediate frames from nearby source frames while maintaining spatial and temporal consistencies. The existing deep-learning-based video frame interpolation methods can be roughly divided…

Kernel interpolation, especially in the context of Gaussian process emulation, is a widely used technique in surrogate modelling, where the goal is to cheaply approximate an input-output map using a limited number of function evaluations.…

In connection with the classical Schwartz kernel theorem, we show that in the framework of Colombeau generalized functions a large class of linear mappings admit integral kernels. To do this, we need to introduce news spaces of generalized…

In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…

In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…

In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of…

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

We address the challenging application of 3D pore scale reactive flow under varying geometry parameters. The task is to predict time-dependent integral quantities, i.e., breakthrough curves, from the given geometries. As the 3D reactive…

In this note we give sufficient conditions for the convergence of the iterative algorithm called weighted-average consensus in directed graphs. We study the discrete-time form of this algorithm. We use standard techniques from matrix theory…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…