Related papers: A Comparison Study of Nonlinear Kernels

The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple…

The min-max kernel is a generalization of the popular resemblance kernel (which is designed for binary data). In this paper, we demonstrate, through an extensive classification study using kernel machines, that the min-max kernel often…

Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…

Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…

The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with…

The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted…

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution…

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…

One of the major challenges for low-rank multi-fidelity (MF) approaches is the assumption that low-fidelity (LF) and high-fidelity (HF) models admit "similar" low-rank kernel representations. Low-rank MF methods have traditionally attempted…

A simple yet effective architectural design of radial basis function neural networks (RBFNN) makes them amongst the most popular conventional neural networks. The current generation of radial basis function neural network is equipped with…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

As recent literature has demonstrated how classifiers often carry unintended biases toward some subgroups, deploying machine learned models to users demands careful consideration of the social consequences. How should we address this…

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…

In deep learning models, learning more with less data is becoming more important. This paper explores how neural networks with normalized Radial Basis Function (RBF) kernels can be trained to achieve better sample efficiency. Moreover, we…

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size…

We study the use of "sign $\alpha$-stable random projections" (where $0<\alpha\leq 2$) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and…

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…