Related papers: On the optimal shape parameter for kernel methods:…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
Recent advances in machine learning have inspired a surge of research into reconstructing specific quantities of interest from measurements that comply with certain physical laws. These efforts focus on inverse problems that are governed by…
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…
Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…
Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…
Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…
Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…
The paper introduces a new characterisation of strictly positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both…
Kernel size selection in Convolutional Neural Networks (CNNs) is a critical but often overlooked design decision that affects receptive field, feature extraction, computational cost, and model accuracy. This paper proposes the Best Kernel…
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…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…