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Tree graphs are routinely used in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to…

Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

Kemeny constant, defined as the expected hitting time of random walks from a source node to a randomly chosen target node, is a fundamental metric in graph data management with many real-world applications. However, computing it exactly on…

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…

Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…

Background: Adaptation technique is a crucial task for analogy based estimation. Current adaptation techniques often use linear size or linear similarity adjustment mechanisms which are often not suitable for datasets that have complex…

We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of…

Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…

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…

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…

We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…

Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

Knowledge graph (KG) embedding techniques use structured relationships between entities to learn low-dimensional representations of entities and relations. The traditional KG embedding techniques (such as TransE and DistMult) estimate these…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…