Related papers: Mirror Descent on Reproducing Kernel Banach Spaces

Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…

The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks correspond to function spaces that are Hilbert spaces, these…

This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in…

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess…

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the…

Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability of the output quadrature formulas are advantages of this…

In this work, we analyze the learnability of reproducing kernel Hilbert spaces (RKHS) under the $L^\infty$ norm, which is critical for understanding the performance of kernel methods and random feature models in safety- and…

Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…

Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin…

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of…

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings…