Related papers: Multilevel branching splitting algorithm for estim…
Autonomous Vehicles (AVs) are often tested in simulation to estimate the probability they will violate safety specifications. Two common issues arise when using existing techniques to produce this estimation: If violations occur rarely,…
Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
We present a different view on stochastic optimization, which goes back to the splitting schemes for approximate solutions of ODE. In this work, we provide a connection between stochastic gradient descent approach and first-order splitting…
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
Mass violence, almost no matter how defined, is (thankfully) rare. Rare events are very difficult to study in a systematic manner. Standard statistical procedures can fail badly and usefully accurate forecasts of rare events often are…
This paper considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for e.g. modelling of credit risk. Previous attempts at designing importance sampling algorithms…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is…
In this work, we propose an algorithm to simulate rare events for electronic circuit design. Our approach heavily relies on a smart use of importance sampling, which enables us to tackle probabilities of the magnitude 10 --10. Not only can…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
Annealed importance sampling (AIS) is a common algorithm to estimate partition functions of useful stochastic models. One important problem for obtaining accurate AIS estimates is the selection of an annealing schedule. Conventionally, an…
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…
In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
This work combines multilevel Monte Carlo (MLMC) with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to a broad class of McKean--Vlasov stochastic…
In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…