Related papers: A Class of Diffusion Algorithms with Logarithmic C…

We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…

In a distributed network environment, the diffusion-least mean squares (LMS) algorithm gives faster convergence than the original LMS algorithm. It has also been observed that, the diffusion-LMS generally outperforms other distributed LMS…

In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The…

Diffusion models have demonstrated powerful performance in generating high-quality images. A typical example is text-to-image generator like Stable Diffusion. However, their widespread use also poses potential privacy risks. A key concern…

Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections. They have achieved success in a multitude of applications such as neuroscience,…

In this paper, we propose a novel leaky least mean square (leaky LMS, LLMS) algorithm which employs a p-norm-like constraint to force the solution to be sparse in the application of system identification. As an extension of the LMS…

We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…

When scaling distributed training, the communication overhead is often the bottleneck. In this paper, we propose a novel SGD variant with reduced communication and adaptive learning rates. We prove the convergence of the proposed algorithm…

In this paper I describe a specialized algorithm for anisotropic diffusion determined by a field of transition rates. The algorithm can be used to describe some interesting forms of diffusion that occur in the study of proton motion in a…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to…

Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to sparse…

In this paper, we propose an efficient numerical implementation of Network Embedding based on commute times, using sparse approximation of a diffusion process on the network obtained by a modified version of the diffusion wavelet algorithm.…

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…

Estimating free energy is a fundamental problem in statistical mechanics. Recently, machine-learning-based methods, particularly the variational autoregressive networks (VANs) have been proposed to minimize variational free energy and to…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio…

In diffusion-based algorithms for adaptive distributed estimation, each node of an adaptive network estimates a target parameter vector by creating an intermediate estimate and then combining the intermediate estimates available within its…

We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are…