Related papers: D2KE: From Distance to Kernel and Embedding
In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…
Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform for various kernel methods in machine learning. The purpose of kernel learning is to learn an appropriate RKHS according to different machine learning scenarios and…
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,…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…
Feature matching is a challenging computer vision task that involves finding correspondences between two images of a 3D scene. In this paper we consider the dense approach instead of the more common sparse paradigm, thus striving to find…
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…
Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
This paper presents a close form solution in Reproducing Kernel Hilbert Space (RKHS) for the famed Wiener filter, which we called the functional Wiener filter(FWF). Instead of using the Wiener-Hopf factorization theory, here we define a new…
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…
Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from…
Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…