Related papers: Low rank estimation of smooth kernels on graphs

Let (V, E) be a graph with vertex set V and edge set E. Let (X, X', Y) \in V \times V \times {-1, 1} be a random triple, where X, X' are independent uniformly distributed vertices and Y is a label indicating whether X, X' are "similar" (Y =…

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…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…

A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for…

We study minimax lower bounds for function estimation problems on large graph when the target function is smoothly varying over the graph. We derive minimax rates in the context of regression and classification problems on graphs that…

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…

Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…

We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…

In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…

Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…

In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph $G$ and a positive integer $k$, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$. Motivated by the kernelization of MMVC…

This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…

A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper. The special structure of low rank kernels with a controlled model size brings sparsity as well as…

We develop a kernel-based approach for estimating the spatially varying Sobolev regularity~$s$ of an unknown $d$-variate function~$f$ from scattered sampling data, which quantifies the degree of local differentiability supported by the…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…