Related papers: Reproducing Kernel Banach Spaces with the l1 Norm …

In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also…

Learning with Fredholm kernel has attracted increasing attention recently since it can effectively utilize the data information to improve the prediction performance. Despite rapid progress on theoretical and experimental evaluations, its…

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

We present sampling theorems for reproducing kernel Banach spaces on Lie groups. Recent approaches to this problem rely on integrability of the kernel and its local oscillations. In this paper we replace the integrability conditions by…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the…

We consider the least-square regression problem with regularization by a block 1-norm, i.e., a sum of Euclidean norms over spaces of dimensions larger than one. This problem, referred to as the group Lasso, extends the usual regularization…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Probably the most important problem in machine learning is the preliminary biasing of a learner's hypothesis space so that it is small enough to ensure good generalisation from reasonable training sets, yet large enough that it contains a…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on…

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…

In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…

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…

The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…

Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…