Related papers: Shapley Effect Estimation using Polynomial Chaos
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…
In this paper, we address the estimation of the sensitivity indices called "Shapley eects". These sensitivity indices enable to handle dependent input variables. The Shapley eects are generally dicult to estimate, but they are easily…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of…
For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
Numerous offline and model-based reinforcement learning systems incorporate world models to emulate the inherent environments. A world model is particularly important in scenarios where direct interactions with the real environment is…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
Machine learning (ML) for transient stability assessment has gained traction due to the significant increase in computational requirements as renewables connect to power systems. To achieve a high degree of accuracy; black-box ML models are…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. Most of these models involve inherent uncertainties that must be assessed to increase the confidence in model predictions…
The analysis of causation is a challenging task that can be approached in various ways. With the increasing use of machine learning based models in computational socioeconomics, explaining these models while taking causal connections into…
In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…
Shapley Values are concepts established for eXplainable AI. They are used to explain black-box predictive models by quantifying the features' contributions to the model's outcomes. Since computing the exact Shapley Values is known to be…
Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…
Verification solutions for uncertainty quantification are presented for time dependent transport problems where $c$, the scattering ratio, is uncertain. The method of polynomial chaos expansions is employed for quick and accurate…
Unsupervised anomaly detection is a challenging problem due to the diversity of data distributions and the lack of labels. Ensemble methods are often adopted to mitigate these challenges by combining multiple detectors, which can reduce…
We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters,…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…