Related papers: Learning Representations using Spectral-Biased Ran…

We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…

Unified graph representation learning aims to generate node embeddings, which can be applied to multiple downstream applications of graph analytics. However, existing studies based on graph neural networks and language models either suffer…

Graph representation learning has become a hot research topic due to its powerful nonlinear fitting capability in extracting representative node embeddings. However, for sequential data such as speech signals, most traditional methods…

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…

Graph embedding techniques have led to significant progress in recent years. However, present techniques are not effective enough to capture the patterns of networks. This paper propose neighbor2vec, a neighbor-based sampling strategy used…

Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In…

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine…

We study lower bounds for the problem of approximating a one dimensional distribution given (noisy) measurements of its moments. We show that there are distributions on $[-1,1]$ that cannot be approximated to accuracy $\epsilon$ in…

Graph embedding techniques are a staple of modern graph learning research. When using embeddings for downstream tasks such as classification, information about their stability and robustness, i.e., their susceptibility to sources of noise,…

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…

Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be…

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node…

We propose local-biased random walks on general networks where a Markovian walker can choose between different types of biases in each node to define transitions to its neighbors depending on their degrees. For this ergodic dynamics, we…

Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by…

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…