Related papers: Adaptive sampling of large deviations
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the…
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…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…