Related papers: Heating Up Quasi-Monte Carlo Graph Random Features…

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…

We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference…

Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of…

In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

Kernel functions for Laplacian integral operators are constructed on $p$-adic analytic manifolds using charts and transition maps from an atlas with connected nerve complex. In the compact case, an operator of Vladimirov-Taibleson type…

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two classes of unbounded C^{1,1} open sets in R^d:…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…

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…

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher diffusion driven algorithm and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the…

We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…

Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…