@article{Eggels_2019,
title = {Quantifying Data Dependencies with Rényi Mutual Information and Minimum Spanning Trees},
author = {Anne W. Eggels and Daan T. Crommelin},
doi = {10.3390/e21020100},
issn = {1099-4300},
year = {2019},
date = {2019-01-22},
journal = {Entropy},
volume = {21},
number = {2},
pages = {100},
publisher = {MDPI AG},
abstract = {In this study, we present a novel method for quantifying dependencies in multivariate datasets, based on estimating the Rényi mutual information by minimum spanning trees (MSTs). The extent to which random variables are dependent is an important question, e.g., for uncertainty quantification and sensitivity analysis. The latter is closely related to the question how strongly dependent the output of, e.g., a computer simulation, is on the individual random input variables. To estimate the Rényi mutual information from data, we use a method due to Hero et al. that relies on computing minimum spanning trees (MSTs) of the data and uses the length of the MST in an estimator for the entropy. To reduce the computational cost of constructing the exact MST for large datasets, we explore methods to compute approximations to the exact MST, and find the multilevel approach introduced recently by Zhong et al. (2015) to be the most accurate. Because the MST computation does not require knowledge (or estimation) of the distributions, our methodology is well-suited for situations where only data are available. Furthermore, we show that, in the case where only the ranking of several dependencies is required rather than their exact value, it is not necessary to compute the Rényi divergence, but only an estimator derived from it. The main contributions of this paper are the introduction of this quantifier of dependency, as well as the novel combination of using approximate methods for MSTs with estimating the Rényi mutual information via MSTs. We applied our proposed method to an artificial test case based on the Ishigami function, as well as to a real-world test case involving an El Nino dataset.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{Eggels2018,
title = {Clustering-based collocation for uncertainty propagation with multivariate dependent inputs},
author = {Anne W. Eggels and Daan T. Crommelin and Jeroen A. S. Witteveen},
url = {https://ir.cwi.nl/pub/27271
https://arxiv.org/abs/1703.06112},
doi = {10.1615/int.j.uncertaintyquantification.2018020215},
year = {2018},
date = {2018-01-01},
journal = {International Journal for Uncertainty Quantification},
volume = {8},
number = {1},
pages = {43–59},
publisher = {Begell House},
abstract = {In this paper, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend the use of collocation methods to uncertainty propagation with multivariate, dependent input, in which the output approximation is piecewise constant on the clusters. The approach is particularly useful in situations where the probability distribution of the input is unknown and only a sample from the input distribution is available. We examine several clustering methods and assess the convergence of collocation based on these methods both theoretically and numerically. We demonstrate good performance of the proposed methods, most notably for the challenging case of nonlinearly dependent inputs in higher dimensions. Numerical tests with input dimension up to 16 are included, using as benchmarks the Genz test functions and a test case from computational fluid dynamics (lid-driven cavity flow). },
keywords = {},
pubstate = {published},
tppubtype = {article}
}