相关论文: Kernel methods in machine learning

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

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…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…

The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Kernel methods in machine learning use a kernel function that takes two data points as input and returns their inner product after mapping them to a Hilbert space, implicitly and without actually computing the mapping. For many kernel…

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…

With the advent of kernel methods, automating the task of specifying a suitable kernel has become increasingly important. In this context, the Multiple Kernel Learning (MKL) problem of finding a combination of pre-specified base kernels…

This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…

Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has…

We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…