Related papers: Importance sampling for metastable and multiscale …
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
Feature selection often leads to increased model interpretability, faster computation, and improved model performance by discarding irrelevant or redundant features. While feature selection is a well-studied problem with many widely-used…
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…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at $0$ for all parameter values. Recently, it has been shown that this chain exhibits…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
We propose here some new sampling algorithms for Path Sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
The transport of scalar quantities passively advected by velocity fields with a small-scale component can be modeled at meso-scale level by means of an effective drift and an effective diffusivity, which can be determined by means of…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…
We discuss the relationships between large deviations in stochastic systems, and "effective interactions" that induce particular rare events. We focus on the nature of these effective interactions in physical systems with many interacting…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…