相关论文: Double-Loop Importance Sampling for McKean--Vlasov…

Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation is computationally difficult because it involves intractable…

The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the…

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…

This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on…

State inference and parameter learning in sequential models can be successfully performed with approximation techniques that maximize the evidence lower bound to the marginal log-likelihood of the data distribution. These methods may be…

Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…

The naive importance sampling (IS) estimator generally does not work well in examples involving simultaneous inference on several targets, as the importance weights can take arbitrarily large values, making the estimator highly unstable. In…

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…

In this paper the choice of the Bernoulli distribution as biased distribution for importance sampling (IS) Monte-Carlo (MC) simulation of linear block codes over binary symmetric channels (BSCs) is studied. Based on the analytical…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

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.…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…

A higher-order change-of-measure multilevel Monte Carlo (MLMC) method is developed for computing weak approximations of the invariant measures of SDE with drift coefficients that do not satisfy the contractivity condition. This is achieved…

This paper considers Importance Sampling (IS) for the estimation of tail risks of a loss defined in terms of a sophisticated object such as a machine learning feature map or a mixed integer linear optimisation formulation. Assuming only…

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…

We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly…