Related papers: Kernel Based Reconstruction for Generalized Graph …
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…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…
Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
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.…
We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As…
Many machine learning techniques have been proposed in the last few years to process data represented in graph-structured form. Graphs can be used to model several scenarios, from molecules and materials to RNA secondary structures. Several…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…