Related papers: Efficient Importance Sampling for Wrong Exit Proba…
The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…
This paper proposes niching importance sampling, a framework that combines concepts from reliability analysis, e.g. Markov chains, importance sampling, and relative cross entropy minimisation, with niching techniques from evolutionary…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
The Improved Cross-Entropy (ICE) method is a powerful tool for estimating failure probabilities in reliability analysis. Its core idea is to approximate the optimal importance-sampling density by minimizing the forward Kullback-Leibler…
We consider the problem of low probability estimation: given a machine learning model and a formally-specified input distribution, how can we estimate the probability of a binary property of the model's output, even when that probability is…
In this paper, we propose a sequential directional importance sampling (SDIS) method for rare event estimation. SDIS expresses a small failure probability in terms of a sequence of auxiliary failure probabilities, defined by magnifying the…
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=1}^{N}{X_i} \leq \gamma)$, via importance sampling (IS). We…
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.…
Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties…
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…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is geometric random walks. We analyze the arithmetic…
The problem of studying rare events is central to many areas of computer simulations. In a recent paper [Kang, P., et al., Nat. Comput. Sci. 4, 451-460, 2024], we have shown that a powerful way of solving this problem passes through the…
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…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
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…
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…
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…
The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm,…
Often, it is required to estimate the probability that a quantity such as toxicity level, plutonium, temperature, rainfall, damage, wind speed, wave size, earthquake magnitude, risk, etc., exceeds an unsafe high threshold. The probability…