Related papers: Learning primal-dual sparse kernel machines

Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform for various kernel methods in machine learning. The purpose of kernel learning is to learn an appropriate RKHS according to different machine learning scenarios and…

The study of Neural Tangent Kernels (NTKs) has provided much needed insight into convergence and generalization properties of neural networks in the over-parametrized (wide) limit by approximating the network using a first-order Taylor…

Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…

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…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our…

Adversarial training and data augmentation with noise are widely adopted techniques to enhance the performance of neural networks. This paper investigates adversarial training and data augmentation with noise in the context of regularized…

Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learning the optimal feature map is often…

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

We introduce the neural tangent kernel (NTK) regime for two-layer neural operators and analyze their generalization properties. For early-stopped gradient descent (GD), we derive fast convergence rates that are known to be minimax optimal…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

Focusing on establishing a mathematical basis for kernel methods in sparse multi-task learning, we explore the theory of vector-valued reproducing kernel Banach spaces (RKBSs) endowed with $\ell_{p,1}$-norms ($1\le p\le +\infty$),…

The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this article, we revisit the formalism of the X-ray transform by considering it as an operator between Reproducing Kernel…