相关论文: Recursive Sampling for the Nystr\"om Method

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…

This paper studies a Nystr\"om type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying…

We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…

We develop two approaches for analyzing the approximation error bound for the Nystr\"{o}m method, one based on the concentration inequality of integral operator, and one based on the compressive sensing theory. We show that the…

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…

The recent discovery of the equivalence between infinitely wide neural networks (NNs) in the lazy training regime and Neural Tangent Kernels (NTKs) (Jacot et al., 2018) has revived interest in kernel methods. However, conventional wisdom…

Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…

Randomized algorithms in numerical linear algebra have proven to be effective in ameliorating issues of scalability when working with large matrices, efficiently producing accurate low-rank approximations. A key remaining challenge,…

The bilateral and nonlocal means filters are instances of kernel-based filters that are popularly used in image processing. It was recently shown that fast and accurate bilateral filtering of grayscale images can be performed using a…

Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted…

This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…

Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…

Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…

We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examine the Nystr\"om method where the subspaces are defined by a…

High computational costs of manifold learning prohibit its application for large point sets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire…

Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In…