Related papers: FKreg: A MATLAB toolbox for fast Multivariate Kern…
This paper presents a novel approach for multi-kernel estimation by enhancing the KernelGAN algorithm, which traditionally estimates a single kernel for the entire image. We introduce Multi-KernelGAN, which extends KernelGAN's capabilities…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
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…
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…
Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has been frequently studied. However, none of the existing…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…
Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals.…
Multimodal image fusion (MMIF) integrates information from different modalities to obtain a comprehensive image, aiding downstream tasks. However, existing research focuses on complementary information fusion and training strategies,…
MRI data is acquired in Fourier space/k-space. Data acquisition is typically performed on a Cartesian grid in this space to enable the use of a fast Fourier transform algorithm to achieve fast and efficient reconstruction. However, it has…
Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…
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…
Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…
Hardware trends favor algorithm designs that maximize data reuse per FLOP. We develop and benchmark high-performance Multipole-to-Local (M2L) translation operators for the kernel-independent Fast Multipole Method (kiFMM), a widely adopted…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…