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

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…

Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…

Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…

In this note, we look at some hypoelliptic operators arising from nilpotent rank 2 Lie algebras. In particular, we concentrate on the diffusion generated by three Brownian motions and their three L\'evy areas, which is the simplest…

Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include…

A data-driven framework is presented, that enables the prediction of quantities, either observations or parameters, given sufficient partial data. The framework is illustrated via a computational model of the deposition of Cu in a Chemical…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

Influence maximization (IM) in real platforms is challenged by incomplete, noisy social graphs and non-stationary diffusion dynamics. We propose SP-GCRL, a social-propagation-aware graph contrastive reinforcement learning framework that…

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 inference methods have recently attracted a great interest from the scientific community, due to the large value they bring in data interpretation and analysis. However, most of the available state-of-the-art methods focus on…

Reinforcement learning (RL) algorithms have been used recently to align diffusion models with downstream objectives such as aesthetic quality and text-image consistency by fine-tuning them to maximize a single reward function under a fixed…

Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…

Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field…

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…

We propose a Gradient Boosting algorithm for learning an ensemble of kernel functions adapted to the task at hand. Unlike state-of-the-art Multiple Kernel Learning techniques that make use of a pre-computed dictionary of kernel functions to…