Related papers: Vector-Valued Native Space Embedding for Adaptive …
A novel kernel-based support vector machine (SVM) for graph classification is proposed. The SVM feature space mapping consists of a sequence of graph convolutional layers, which generates a vector space representation for each vertex,…
The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…
Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…
Robust visual place recognition (VPR) requires scene representations that are invariant to various environmental challenges such as seasonal changes and variations due to ambient lighting conditions during day and night. Moreover, a…
This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties…
In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we…
For many quantum systems intended for information processing, one detects the logical state of a qubit by integrating a continuously observed quantity over time. For example, ion and atom qubits are typically measured by driving a cycling…
Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…
In this paper we construct and theoretically analyse group equivariant convolutional kernel networks (CKNs) which are useful in understanding the geometry of (equivariant) CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs).…
In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This…
This paper describes an adaptive method in continuous time for the estimation of external fields by a team of $N$ agents. The agents $i$ each explore subdomains $\Omega^i$ of a bounded subset of interest $\Omega\subset X := \mathbb{R}^d$.…
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on…