Related papers: Enhanced Importance Sampling through Latent Space …
A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of…
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…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap…
Importance sampling is a widely used technique to estimate properties of a distribution. This paper investigates trading-off some bias for variance by adaptively winsorizing the importance sampling estimator. The novel winsorizing…
In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein…
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…
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…
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 describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency…
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…
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…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm…
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…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
This paper provides an introductory overview of how one may employ importance sampling effectively as a tool for solving stochastic optimization formulations incorporating tail risk measures such as Conditional Value-at-Risk. Approximating…