Related papers: Rare Events in Random Geometric Graphs
This paper considers the classical problem of sampling with Monte Carlo methods a target rare event distribution defined by a score function that is very expensive to compute. We assume we can build using evaluations of the true score, an…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive…
We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in determin-istic dynamical systems. We demonstrate that the genealogical particle analysis algorithms can…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function $nf(\cdot)$, where $n\in \mathbb{N}$, and $f$ is a probability density…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the…
We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…
Let $[\mathcal{P}]$ be the points of a Poisson process on $\mathbb{R}^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set…
Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be…
This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow to accurately compute…
In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting…
In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of…
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis of rare events is a computationally challenging problem,…
Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct Metropolis- Hastings Monte Carlo methods that can…
The often debated issue of `ratios of small numbers of events' is approached from a probabilistic perspective, making a clear distinction between the predictive problem (forecasting numbers of events we might count under well stated…