Related papers: Kernel approximation on algebraic varieties

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…

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 present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Kernels ensuing from tree ensembles such as random forest (RF) or gradient boosted trees (GBT), when used for kernel learning, have been shown to be competitive to their respective tree ensembles (particularly in higher dimensional…

Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…

Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the…

We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a…

An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…

Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…

Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…

Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…