Related papers: Random walks on graphs with interval weights and p…
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…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing…
On a connected finite graph, we propose an evolution of weights including Ollivier's Ricci flow as a special case. During the evolution process, on each edge, the speed of change of weight is exactly the difference between the Wasserstein…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…
Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper…
A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…