Related papers: Numerical Estimation of Limiting Large-Deviation R…

Recent success in Deep Reinforcement Learning (DRL) methods has shown that policy optimization with respect to an off-policy distribution via importance sampling is effective for sample reuse. In this paper, we show that the use of…

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that…

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…

We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop…

We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance…

Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…

Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…

Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…

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…

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

The bifurcation method is a way to do rare event sampling -- to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double…

Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…

We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation…

We study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a…

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…

In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…

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…