Related papers: Discovering the Unknowns: A First Step

A fundamental task in science is to determine the underlying causal relations because it is the knowledge of this functional structure what leads to the correct interpretation of an effect given the apparent associations in the observed…

Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…

A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

In this paper a data mining approach for variable selection and knowledge extraction from datasets is presented. The approach is based on unguided symbolic regression (every variable present in the dataset is treated as the target variable…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

One critical challenge of time-series modeling is how to learn and quickly correct the model under unknown distribution shifts. In this work, we propose a principled framework, called LiLY, to first recover time-delayed latent causal…

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…

Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently…

Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…

Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…

Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…

A trend in all scientific disciplines, based on advances in technology, is the increasing availability of high dimensional data in which are buried important information. A current urgent challenge to statisticians is to develop effective…

Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…