arXiv research

Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.

Linear time algorithm for random walk kernels on sparse graphs.

Repelling random walks improve graph-based sampling efficiency.

A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.

A new method improves graph random features with quasi-Monte Carlo techniques.

New walk extraction strategies improve node embeddings in KGs.

New random walk results on rank one symmetric spaces.

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed…

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, graphs these have some counter-intuitive properties, specifically in the limit of lar…

Study uniform convergence of random walk Laplacians to diffusion Laplacian on smooth manifolds.

Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix factorization and random walk-based models. In this paper, we aim to bring toge…

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a new dual-tree based variational approach for approximating the transition matrix…

Model place cells as spatial embeddings for efficient path planning and cognitive map construction.

This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to buy and selling the next period, with no shorting, and furthermore for weak conv…

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact an…

Study large deviations in random walks on Lie groups.

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few…

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the n…

Quantum walks blend patterns into splines when averaged.

Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.

Random walks on cell complexes link to Laplacians and Novikov-Shubin invariants.

Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.

Random walks on metric spaces embed quasi-isometrically into the space.

This work estimates edge weights of edge-reinforced random walks using observed data.

New proof shows rapid mixing for random walks on nilmanifolds.

Random walks on hyperbolic spaces show linear growth in translation lengths.

Study random walks on groups with superlinear divergent geodesics.

Study random walks on sub-Riemannian manifolds using retractions.

The paper examines random walks on metric spaces and finds commensurable subgroups.

Random walks on free groups reveal asymmetric expansion factors.

Survey on random walks on mapping class groups and their properties.

Deviation inequalities and limit laws for random walks on metric spaces.

Random walks on Fuchsian Schottky groups have harmonic measures with lower dimension.

UniNet efficiently learns network representations from large graphs.

The study of random walks on hyperbolic spaces and Teichmüller spaces, proving central limit theorems and geodesic tracking.

Uniform drift estimates found for random walks on graph products.

A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically independent, and converges to the product of the harmonic an…

We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of the graph along a path, and the next iterate is chosen from the neighbors of the…

Geodesic walks converge to Brownian motion on Finsler manifolds.

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex wei…

TSAW improves MCMC integral estimation with faster convergence.

We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular we prove that if a convergence group $G$ acts on a compact metrizable space $M$ with the convergence property then we can provide $G\cup M$ with a compact topology such that random walks on $G$ converge a…

For any pseudo-Anosov diffeomorphism on a closed orientable surface $S$ of genus greater than one, it is known by the work of Bers and Thurston that the topological entropy agrees with the translation distance on the Teichmüller space with respect to the Teichmüller metric. In this paper, we consider random walks on th…

DM uses semigroup property to tune diffusion time for better data analysis.

Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of …

Abstract: Nonlinear random walk with distributionally robust transition probabilities.

Study large deviations and speed of random walks in hyperbolic spaces.

Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. W…