Related papers: Deep importance sampling using tensor trains 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…

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…

General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…

The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model.…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…

Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…

We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…

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…

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…

In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…

Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult…

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 consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…