Related papers: A Generalized Kernel Approach to Structured Output…

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…

Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…

We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…

This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model…

Compositional generalization (the ability to respond correctly to novel combinations of familiar components) is thought to be a cornerstone of intelligent behavior. Compositionally structured (e.g. disentangled) representations support this…

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Many real-world applications are associated with structured data, where not only input but also output has interplay. However, typical classification and regression models often lack the ability of simultaneously exploring high-order…

Motivated by the needs from an airline crew scheduling application, we introduce structured convolutional kernel networks (Struct-CKN), which combine CKNs from Mairal et al. (2014) in a structured prediction framework that supports…

This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…