Related papers: Marginalization for rare event simulation in switc…
We consider a standard splitting algorithm for the rare-event simulation of overflow probabilities in any subset of stations in a Jackson network at level n, starting at a fixed initial position. It was shown in DeanDup09 that a subsolution…
We study rare-event simulation for a class of problems where the target hitting sets of interest are defined via modern machine learning tools such as neural networks and random forests. This problem is motivated from fast emerging studies…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…
Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections)…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
A leading goal for climate science and weather risk management is to accurately model both the physics and statistics of extreme events. These two goals are fundamentally at odds: the higher a computational model's resolution, the more…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
We briefly review simulation schemes for the investigation of rare transitions and we resume the recently introduced Transition Interface Sampling, a method in which the computation of rate constants is recast into the computation of fluxes…
A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…
Combining the increasing availability and abundance of healthcare data and the current advances in machine learning methods have created renewed opportunities to improve clinical decision support systems. However, in healthcare risk…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…