Related papers: Instantons for rare events in heavy-tailed distrib…

Adaptive importance sampling (AIS) algorithms are widely used to approximate expectations with respect to complicated target probability distributions. When the target has heavy tails, existing AIS algorithms can provide inconsistent…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…

Based on the new valley equation, we propose the most plausible method for constructing instanton-like configurations in the theory where the presence of a mass scale prevents the existence of the classical solution with a finite radius. We…

In this paper, we develop a computational approach for computing most likely trajectories describing rare events that correspond to the emergence of non-dominant genotypes. This work is based on the large deviations approach for discrete…

The validity of the instanton analysis approach is tested numerically in the case of the diffraction-amplification problem $\partial_z\psi -\frac{i}{2m}\partial^2_{x^2} \psi =g\vert S\vert^2\, \psi$ for $\ln U\gg 1$, where…

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…

We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

In this work, we study the convergence \emph{in high probability} of clipped gradient methods when the noise distribution has heavy tails, ie., with bounded $p$th moments, for some $1<p\le2$. Prior works in this setting follow the same…

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…

The ability to detect and classify rare occurrences in images has important applications - for example, counting rare and endangered species when studying biodiversity, or detecting infrequent traffic scenarios that pose a danger to…

Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…

For noninteracting particles moving in a Gaussian random potential, there exists a disagreement in the literature on the asymptotic expression for the density of states in the tail of the band. We resolve this discrepancy. Further we…

This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on…

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to computing thermal reaction rates for complex molecular systems including quantum tunneling effects. There have been a number of attempts to…

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…