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The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly…
Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable…
Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL)…
We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels…
The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
We consider the problem of robust estimation involving filtering and smoothing for nonlinear state space models which are disturbed by heavy-tailed impulsive noises. To deal with heavy-tailed noises and improve the robustness of the…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…
The Maximum Mean Discrepancy (MMD) is a cornerstone statistic for nonparametric two-sample testing, but its test power is dictated entirely by the chosen kernel. Because any fixed kernel inherently fails to distinguish certain…
Two-dimensional singular decomposition (2DSVD) has been widely used for image processing tasks, such as image reconstruction, classification, and clustering. However, traditional 2DSVD algorithm is based on the mean square error (MSE) loss,…
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for…