相关论文: Kernel Identities and Vectorial Regularization

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

The use of second order boundary kernels for distribution function estimation was recently addressed in the literature (C. Tenreiro, 2013, Boundary kernels for distribution function estimation, REVSTAT-Statistical Journal, 11, 169-190). In…

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…

We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel $\kappa$, which translates naturally into kernels between histograms or clouds of points. We first cover…

Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…

Anomaly detection is necessary for proper and safe operation of large-scale systems consisting of multiple devices, networks, and/or plants. Those systems are often characterized by a pair of multivariate datasets. To detect anomaly in such…

The Tanimoto kernel (Jaccard index) is a well known tool to describe the similarity between sets of binary attributes. It has been extended to the case when the attributes are nonnegative real values. This paper introduces a more general…

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel…

Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the…

In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…

Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…

The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to extract non-linear information and achieve optimal clustering by optimizing base kernel matrices. Current methods enhance information diversity and reduce redundancy…

The ability to generalize to unseen domains is crucial for machine learning systems deployed in the real world, especially when we only have data from limited training domains. In this paper, we propose a simple and effective regularization…

Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…

Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…