Related papers: Quasi-Monte Carlo Graph Random Features
We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the…
Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…
$M$-Lipschitz mappings of graphs (or equivalently graph-indexed random walks) are a generalization of standard random walk on $\mathbb{Z}$. For $M \in \N$, an \emph{$M$-Lipschitz mapping} of a connected rooted graph $G = (V,E)$ is a mapping…
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…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
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…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…
Graphs are useful structures that can model several important real-world problems. Recently, learning graphs have drawn considerable attention, leading to the proposal of new methods for learning these data structures. One of these studies…
Many real-world datasets can be represented in the form of a graph whose edge weights designate similarities between instances. A discrete Gaussian random field (GRF) model is a finite-dimensional Gaussian process (GP) whose prior…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…
Random walk based sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as GMD modify the topology of…
In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…
Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…
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…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…
The radial basis function (RBF) and quasi Monte Carlo (QMC) methods are two very promising schemes to handle high-dimension problems with complex and moving boundary geometry due to the fact that they are independent of dimensionality and…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…