Related papers: Geometric Kernel Interpolation and Regression
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…
Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…
Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we…
One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…