Related papers: Variational approach to rare event simulation usin…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
Feature attribution methods, or saliency maps, are one of the most popular approaches for explaining the decisions of complex machine learning models such as deep neural networks. In this study, we propose a stochastic optimization approach…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample…
We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. We first study a sample-based approximation of the collision probabilities and use this approximation…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed. However, in a number of settings, we…
Downscaling aims to link the behaviour of the atmosphere at fine scales to properties measurable at coarser scales, and has the potential to provide high resolution information at a lower computational and storage cost than numerical…