Related papers: Learning Reconstructive Embeddings in Reproducing …
This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L^2(S^2) function space of finite energy signals. In…
An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is developed. It is based on an approximation of the generator of…
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…
Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
This paper presents a novel approach to formulating the actor-critic method for optimal control by casting policy iteration in reproducing kernel Hilbert spaces (RKHSs -- also known as native spaces). By tailoring the reproducing kernel and…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…
We consider the regret minimization problem in reinforcement learning (RL) in the episodic setting. In many real-world RL environments, the state and action spaces are continuous or very large. Existing approaches establish regret…
The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed…
We propose a new, nonparametric approach to estimating the value function in reinforcement learning. This approach makes use of a recently developed representation of conditional distributions as functions in a reproducing kernel Hilbert…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
In this paper, we illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…