82 citations · 433 across the 35 of their papers we have counts for
38 papers
Differentiable Kernel Ridge Regression for Deep Learning Pipelines
Jean-Marc Mercier, Gabriele Santin
Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods…
Piecewise linear interpolation via kernels
Toni Karvonen, Gabriele Santin, Tizian Wenzel
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space is equipped with a suitable inner product…
Refined rates of convergence for target-data dependent greedy generalized interpolation with Sobolev kernels
Bernard Haasdonk, Gabriele Santin, Tizian Wenzel +1
Greedy methods have recently been successfully applied to generalized kernel interpolation, or the recovery of a function from data stemming from the evaluation of linear functiona…
On the optimal shape parameter for kernel methods: Sharp direct and inverse statements
Tizian Wenzel, Gabriele Santin
The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a t…
Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems
Bernard Haasdonk, Gabriele Santin, Tizian Wenzel
We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpola…
General superconvergence for kernel-based approximation
Toni Karvonen, Gabriele Santin, Tizian Wenzel
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproduc…
An algorithm for a constrained P-spline
Rosanna Campagna, Serena Crisci, Gabriele Santin +2
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticia…
Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
Jonghyeon Lee, Boumediene Hamzi, Boya Hou +3
The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both d…
On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces
Gabriele Santin, Tizian Wenzel, Bernard Haasdonk
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to cer…
Interpolation with the polynomial kernels
Giacomo Elefante, Wolfgang Erb, Francesco Marchetti +3
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are r…
Equally spaced points are optimal for Brownian Bridge kernel interpolation
Gabriele Santin
In this paper we show how ideas from spline theory can be used to construct a local basis for the space of translates of a general iterated Brownian Bridge kernel $k_{β,\varepsilon…
Adaptive meshfree approximation for linear elliptic partial differential equations with PDE-greedy kernel methods
Tizian Wenzel, Daniel Winkle, Gabriele Santin +1
We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss th…
Reprogramming FairGANs with Variational Auto-Encoders: A New Transfer Learning Model
Beatrice Nobile, Gabriele Santin, Bruno Lepri +1
Fairness-aware GANs (FairGANs) exploit the mechanisms of Generative Adversarial Networks (GANs) to impose fairness on the generated data, freeing them from both disparate impact an…
Stability of convergence rates: Kernel interpolation on non-Lipschitz domains
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case…
Greedy algorithms for learning via exponential-polynomial splines
Rosanna Campagna, Stefano De Marchi, Emma Perracchione +1
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines,…
HJB-RBF based approach for the control of PDEs
Alessandro Alla, Hugo Oliveira, Gabriele Santin
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid mak…
Convergence analysis for image interpolation in terms of the cSSIM
Francesco Marchetti, Gabriele Santin
Assessing the similarity of two images is a complex task that attracts significant efforts in the image processing community. The widely used Structural Similarity Index Measure (S…
Analysis of target data-dependent greedy kernel algorithms: Convergence rates for -, - and -greedy
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Data-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this expe…
Analysis of Structured Deep Kernel Networks
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particula…
Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows
Tizian Wenzel, Marius Kurz, Andrea Beck +2
Standard kernel methods for machine learning usually struggle when dealing with large datasets. We review a recently introduced Structured Deep Kernel Network (SDKN) approach that…
Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization
Salvatore Cuomo, Wolfgang Erb, Gabriele Santin
The inference of novel knowledge, the discovery of hidden patterns, and the uncovering of insights from large amounts of data from a multitude of sources make Data Science (DS) to…
Kernel methods for center manifold approximation and a data-based version of the Center Manifold Theorem
Bernard Haasdonk, Boumediene Hamzi, Gabriele Santin +1
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows…
Biomechanical surrogate modelling using stabilized vectorial greedy kernel methods
Bernard Haasdonk, Tizian Wenzel, Gabriele Santin +1
Greedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization of…
Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces
Gabriele Santin, Toni Karvonen, Bernard Haasdonk
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature r…