Related papers: Importance Sampling for rare events and conditione…

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…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

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.…

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…

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…

We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…

Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the…

In many stochastic problems, the output of interest depends on an input random vector mainly through a single random variable (or index) via an appropriate univariate transformation of the input. We exploit this feature by proposing an…

Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…

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 propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…

Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers.…

We consider importance sampling for estimating the probability that a light-tailed $d$-dimensional random walk exits through one of many disjoint rare-event regions before reaching an anticipated target. This problem arises in sequential…

Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling methods based on the exponential tilting for these models suffers from the difficulties in computing the eigenvalues and…

We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed…

Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…

Automated Vehicle (AV) validation based on simulated testing requires unbiased evaluation and high efficiency. One effective solution is to increase the exposure to risky rare events while reweighting the probability measure. However,…