相关论文: Global sensitivity analysis and Wasserstein spaces

Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity…

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in…

Sensitivity analyses of simulation ensembles determine how simulation parameters influence the simulation's outcome. Commonly, one global numerical sensitivity value is computed per simulation parameter. However, when considering 3D spatial…

This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such…

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences via a global sensitivity analysis (GSA). However, these…

Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…

Development of new multiscale mathematical models often entails considerable complexity and multiple undetermined parameters, typically arising from closure relations. To enable reliable simulations, one must quantify how uncertain physical…

Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…

We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…

Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…

We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein-Procrustes distance, where the in-between cluster variability is penalised…

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…

It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we…

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…

Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…

Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. The…

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…