Related papers: Ergodic Limits, Relaxations, and Geometric Propert…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such…
We consider a Metropolis--Hastings method with proposal $\mathcal{N}(x, hG(x)^{-1})$, where $x$ is the current state, and study its ergodicity properties. We show that suitable choices of $G(x)$ can change these compared to the Random Walk…
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…
We consider the problem of detecting a random walk on a graph, based on observations of the graph nodes. When visited by the walk, each node of the graph observes a signal of elevated mean, which we assume can be different across different…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
Unsupervised approaches to learning in neural networks are of substantial interest for furthering artificial intelligence, both because they would enable the training of networks without the need for large numbers of expensive annotations,…
In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Such temporal networks (or edge streams) consist of a sequence of timestamped edges and are seemingly ubiquitous. Despite the importance of…
Learning good quality neural graph embeddings has long been achieved by minimizing the point-wise mutual information (PMI) for co-occurring nodes in simulated random walks. This design choice has been mostly popularized by the direct…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
The goal of network embedding is to transform nodes in a network to a low-dimensional embedding vectors. Recently, heterogeneous network has shown to be effective in representing diverse information in data. However, heterogeneous network…
In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social…
Digital presence in the world of online social media entails significant privacy risks. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such…
Analysis of social networks with limited data access is challenging for third parties. To address this challenge, a number of studies have developed algorithms that estimate properties of social networks via a simple random walk. However,…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…