Related papers: The kernel method for lattice paths below a line o…

An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…

A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…

We develop a complete theory for the combinatorics of walk-counting on a directed graph in the case where each backtracking step is downweighted by a given factor. By deriving expressions for the associated generating functions, we also…

Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…

We show the existence of an exact mimicking network of $k^{O(\log k)}$ edges for minimum multicuts over a set of terminals in an undirected graph, where $k$ is the total capacity of the terminals, as well as a method for computing a…

We discuss the structure of positive definite kernels in terms of operator models. In particular, we introduce two models, one of Hessenberg type and another one that we call near triangular. These models produce parametrizations of the…

We prove new bijections between different variants of Dyck paths and integer compositions, which give combinatorial explanations of their simple counting formula $4^{n-1}$. These give relations between different statistics, such as the…

In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which…

Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…

Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

We introduce a new kernelization tool, called rainbow matching technique}, that is appropriate for the design of polynomial kernels for packing problems and their hitting counterparts. Our technique capitalizes on the powerful combinatorial…

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…

We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical…

We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…