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In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of $n$ agents collaboratively minimize the average of the local objective…

Optimization and Control · Mathematics 2025-03-27 Kun Huang , Shi Pu , Angelia Nedić

Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…

Probability · Mathematics 2014-07-25 Mark M. Meerschaert , Peter Straka

Designing effective algorithms for community detection is an important and challenging problem in {\em large-scale} graphs, studied extensively in the literature. Various solutions have been proposed, but many of them are centralized with…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-04-17 Reza Fathi , Anisur Rahaman Molla , Gopal Pandurangan

In this paper, we consider distributed optimization problems where $n$ agents, each possessing a local cost function, collaboratively minimize the average of the local cost functions over a connected network. To solve the problem, we…

Optimization and Control · Mathematics 2023-03-24 Kun Huang , Xiao Li , Andre Milzarek , Shi Pu , Junwen Qiu

The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…

Computer Vision and Pattern Recognition · Computer Science 2013-06-06 Pierre-Yves Baudin , Danny Goodman , Puneet Kumar , Noura Azzabou , Pierre G. Carlier , Nikos Paragios , M. Pawan Kumar

We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of…

Numerical Analysis · Mathematics 2024-03-12 Chiheb Ben Hammouda , Nadhir Ben Rached , Raúl Tempone , Sophia Wiechert

Item-based models are among the most popular collaborative filtering approaches for building recommender systems. Random walks can provide a powerful tool for harvesting the rich network of interactions captured within these models. They…

Information Retrieval · Computer Science 2020-10-07 Athanasios N. Nikolakopoulos , George Karypis

We consider a distributed stochastic optimization problem that is solved by a decentralized network of agents with only local communication between neighboring agents. The goal of the whole system is to minimize a global objective function…

Optimization and Control · Mathematics 2022-11-10 Alexander Rogozin , Mikhail Bochko , Pavel Dvurechensky , Alexander Gasnikov , Vladislav Lukoshkin

Discriminative Random Walks (DRWs) are a simple yet powerful tool for semi-supervised node classification, but their theoretical foundations remain fragmentary. We revisit DRWs through the lens of information geometry, treating the family…

Machine Learning · Statistics 2026-02-10 Masanari Kimura

The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…

Computer Vision and Pattern Recognition · Computer Science 2013-09-02 Pierre-Yves Baudin , Danny Goodman , Puneet Kumar , Noura Azzabou , Pierre G. Carlier , Nikos Paragios , M. Pawan Kumar

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them…

Machine Learning · Statistics 2026-04-16 Xingran Chen , Parimal Parag , Rohit Bhagat , Zonghong Liu , Salim El Rouayheb

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of $\tilde{\mathcal{O}}(n^{7}T^{-1/2})$ after $T$ queries for a convex bounded function $f:{\mathbb R}^n\to{\mathbb R}$. The method is…

Machine Learning · Computer Science 2014-02-13 Tengyuan Liang , Hariharan Narayanan , Alexander Rakhlin

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many…

Machine Learning · Statistics 2023-11-27 Shin Matsushima , Hyokun Yun , Xinhua Zhang , S. V. N. Vishwanathan

This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where…

Optimization and Control · Mathematics 2020-08-21 Xiaoming Duan , Francesco Bullo

In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…

Computational Physics · Physics 2018-08-20 Gurtek Gill , Peter Straka

We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…

Optimization and Control · Mathematics 2020-10-06 Adel Aghajan , Behrouz Touri

The random walk Metropolis (RWM) is one of the most common Markov chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with…

Methodology · Statistics 2010-11-30 Chris Sherlock , Paul Fearnhead , Gareth O. Roberts

The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…

Data Structures and Algorithms · Computer Science 2021-12-15 John Kallaugher , Michael Kapralov , Eric Price

This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…

Social and Information Networks · Computer Science 2017-11-10 Buddhika Nettasinghe , Vikram Krishnamurthy