Related papers: Efficient Rare-Event Simulation for Random Geometr…

In dense Erd\H{o}s-R\'enyi random graphs, we are interested in the events where large numbers of a given subgraph occur. The mean behavior of subgraph counts is known, and only recently were the related large deviations results discovered.…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…

The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap…

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model.…

Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…

The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…

In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…

In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein…

In this paper, we study rare events in spherical and Gaussian random geometric graphs in high dimensions. In these models, the vertices correspond to points sampled uniformly at random on the $d$ dimensional unit sphere or correspond to $d$…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we…

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…