相关论文: On Kernel Design for Regularized Volterra Series I…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…

This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

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…

Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model.…

We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary…

Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…

Recently, non-stationary spectral kernels have drawn much attention, owing to its powerful feature representation ability in revealing long-range correlations and input-dependent characteristics. However, non-stationary spectral kernels are…

Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…

We make an attempt to understanding convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall…

This study proposes a novel framework for spectral unmixing by using 1D convolution kernels and spectral uncertainty. High-level representations are computed from data, and they are further modeled with the Multinomial Mixture Model to…

Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not…

A method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular,…