Related papers: Borel Kernels and their Approximation, Categorical…

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

There is a very general picture emerging that conjecturally describes what happens to the representation theory of a vertex algebra $\mathcal{V}$ if we pass to the kernel $\mathcal{W}$ of a set of screening operators. Namely, the screening…

We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…

We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting…

Random features have been introduced to scale up kernel methods via randomization techniques. In particular, random Fourier features and orthogonal random features were used to approximate the popular Gaussian kernel. Random Fourier…

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that…

Some sharp results related to the convergence of means and families of operators generated by the generalized Bochner-Riesz kernels are obtained. The exact order of approximation of functions by these methods via $K$-functional (or its…

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

We propose efficient random features for approximating a new and rich class of kernel functions that we refer to as Generalized Zonal Kernels (GZK). Our proposed GZK family, generalizes the zonal kernels (i.e., dot-product kernels on the…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…

With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…

A general, {\em rectangular} kernel matrix may be defined as $K_{ij} = \kappa(x_i,y_j)$ where $\kappa(x,y)$ is a kernel function and where $X=\{x_i\}_{i=1}^m$ and $Y=\{y_i\}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way…

This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…