arXiv research

Paper proves non-equivalence of RKHS stability and kernel absolute summability.

Embedding RL policies in RKHS for robustness and theoretical guarantees.

Paper proposes a method to stabilize estimation of KL divergence using a discriminator in RKHS.

The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional represen…

New method simplifies tomographic reconstruction using RKHS.

Unified kernel framework extends to stochastic systems, improving numerical stability.

Develops a new method for learning non-parametric DAGs using RKHS.

Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(…

The study analyzes the performance of a nonparametric estimator for dynamical systems.

ULFS-KDPE estimates parameters efficiently without influence functions.

State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain over-parameterized regime, the learning dynamics of gradient descent are governed …

New algorithms tackle RKHS bandits with reduced complexity and improved performance.

Constructs non-asymptotic confidence regions for unknown functions in RKHS.

Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm. When the data fit is measured using a quadratic loss, this estimator has a know…

Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by leveraging the kernel trick. Classic kernel methods learn a single layer of nonl…

This paper develops a general framework for metric learning in RKHS with theoretical guarantees.

New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.

Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.

Paper introduces RKHM for more explicit variable structures analysis.

This work analyzes the role of data augmentation in self-supervised learning using RKHS approximation and regression.

We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion spaces. We illustrate the general results with…

Neural networks can approximate functionals on RKHS with error bounds.

Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.

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 introduced regression models in an approximation theory view. Algorithmically, we c…

New approach to supervised learning in RKHS and vvRKHS using $C^*$-algebras.

Study evaluates RKHS choices for assessing graph models using KSD tests.

Develops inverse unscented Kalman filter for non-linear systems.

A new method for learning function parameters in operators using data-adaptive RKHS.

New analysis shows a gap between Gaussian RKHS and neural networks on unbounded domains.

Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.

Wide neural networks can outperform kernel methods in certain tasks.

Paper explores RKHS properties for derivative and integral operators.

Learn ODEs from noisy data using RKHS and optimization.

Develops RKHS framework for analyzing tree ensembles.

Adapts RKHS methods to estimate density ratios with optimal error.

Study on how sampling works for complex data functions.

This paper improves signal reconstruction using determinantal sampling from random nodes.

New algorithm optimizes functions in Matérn kernel RKHS with noisy feedback.

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…

Kernel $ε$-Greedy optimizes multi-armed bandits with covariates for sub-linear regret.

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…

A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in homogeneity testing, independence testing, dimensionality reduction, etc., with the re…

Paper introduces RKHM and KME for richer data analysis.

Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo kernel, is needed to learn any function in complex-valued fields. Accordingly, we…

Develops a new framework for estimating joint probability distributions.

Research aims to improve confidence intervals for RKHS elements in online learning.