Related papers: Generalized RBF kernel for incomplete data

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or…

In biological data, it is often the case that observed data are available only for a subset of samples. When a kernel matrix is derived from such data, we have to leave the entries for unavailable samples as missing. In this paper, we make…

Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…

Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…

Quantum computing promises to revolutionize machine learning, offering significant efficiency gains in tasks such as clustering and distance estimation. Additionally, it provides enhanced security through fundamental principles like the…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

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…

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…

Missing responses is a missing data format in which outcomes are not always observed. In this work we develop kernel machines that can handle missing responses. First, we propose a kernel machine family that uses mainly the complete cases.…

Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Although empirical studies have confirmed the effectiveness of spectrum-based fault localization (SBFL) techniques, their performance may be degraded due to presence of some undesired circumstances such as the existence of coincidental…

In recent years, the random vector functional link (RVFL) network has gained significant popularity in hyperspectral image (HSI) classification due to its simplicity, speed, and strong generalization performance. However, despite these…

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…

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…

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

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…