Related papers: Quantifying dependencies for sensitivity analysis …

Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…

We explore a supervised machine learning approach to estimate the entanglement entropy of multi-qubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's…

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

R\'enyi transfer entropy (RTE) is a generalization of classical transfer entropy that replaces Shannon's entropy with R\'enyi's information measure. This, in turn, introduces a new tunable parameter $\alpha$, which accounts for sensitivity…

We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete…

Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used…

A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…

Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…

Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…

Entropy quantifies the number of bits required to store objects under certain given assumptions. While this is a well established concept for strings, in the context of tries the state-of-the-art regarding entropies is less developed. The…

Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…

In this paper, we study weakly dynamic undirected graphs, that can be used to represent some logistic networks. The goal is to deliver all the delivery points in the network. The network exists in a mostly stable environment, except for a…

In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of…

We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations…

We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the…

In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained…