Related papers: Bayesian Approach for Radial Kernel Parameter Tuni…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
We mainly concerned with a decoupled fractional Laplacian wave equation in this paper. A new time-space domain radial basis function (RBF) collocation method is introduced to solve the fractional wave equation, which describes seismic wave…
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…
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
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…
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The…
Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is…
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…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
The standard beam management procedure in 5G requires the user equipment (UE) to periodically measure the received signal reference power (RSRP) on each of a set of beams proposed by the basestation (BS). It is prohibitively expensive to…
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…
This paper develops a Bayesian optimal experimental design for robot kinematic calibration on ${\mathbb{S}^3 \!\times\! \mathbb{R}^3}$. Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
Semiconductor device models are essential to understand the charge transport in thin film transistors (TFTs). Using these TFT models to draw inference involves estimating parameters used to fit to the experimental data. These experimental…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…