Related papers: Fast Multiscale Diffusion on Graphs

We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…

Diffusion models have been increasingly used as strong generative priors for solving inverse problems such as super-resolution in medical imaging. However, these approaches typically utilize a diffusion prior trained at a single scale,…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…

Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for…

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…

The application of the diffusion in many computer vision and artificial intelligence projects has been shown to give excellent improvements in performance. One of the main bottlenecks of this technique is the quadratic growth of the kNN…

The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…

The challenges of graph stream algorithms are twofold. First, each edge needs to be processed only once, and second, it needs to work on highly constrained memory. Diffusion degree is a measure of node centrality that can be calculated (for…

Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs. In this paper, we study…

This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…

The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…

Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent…

Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen's and…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and…