Related papers: Large deviations principle for the Adaptive Multil…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle system, where at each step, the $k$ less well-adapted…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting…
This work investigates the computational burden of pricing binary options in rare event regimes and introduces an adaptation of the adaptive multilevel splitting (AMS) method for financial derivatives. Standard Monte Carlo becomes…
The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, 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…
Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set $B$ before another set $A$, and it is assumed that this probability satisfies a large…
We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
Transitional localised turbulence in shear flows is known to either decay to an absorbing laminar state or proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number…
Computing accurate rate constants for catalytic events occurring at the surface of a given material represents a challenging task with multiple potential applications in chemistry. To address this question, we propose an approach based on a…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012)…
Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several…
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…