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Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…

Kernel functions are vital ingredients of several machine learning algorithms, but often incur significant memory and computational costs. We introduce an approach to kernel approximation in machine learning algorithms suitable for…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Kernel normalization methods have been employed to improve robustness of optimization methods to reparametrization of convolution kernels, covariate shift, and to accelerate training of Convolutional Neural Networks (CNNs). However, our…

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

Kernel ridge regression, in general, is expensive in memory allocation and computation time. This paper addresses low rank approximations and surrogates for kernel ridge regression, which bridge these difficulties. The fundamental…

The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…

We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N \log^2 N $ work), we can solve linear systems with this matrix with $N \log N…

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

Deep kernel map networks have shown excellent performances in various classification problems including image annotation. Their general recipe consists in aggregating several layers of singular value decompositions (SVDs) -- that map data…