* Chaos, Solitons & Fractals - Feb. 7, 2024*

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback–Leibler divergence between two sparsely sampled discrete distributions, is even harder. Here, we propose a fast, semi-analytical estimator for sparsely sampled distributions. Its derivation...

* Proc. Natl. Acad. Sci. USA - Dec. 7, 2023*

Complex networked systems often exhibit higher-order interactions, beyond dyadic interactions, which can dramatically alter their observed behavior. Consequently, understanding hypergraphs from a structural perspective has become increasingly important. Statistical, group-based inference approaches are well suited for unveiling the underlying community structure and predicting unobserved interactions. However, these approaches often rely...

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true...

Cells, ecosystems and economies are examples of complex systems. In complex systems, individual components interact with each other, usually in nonlinear ways, giving rise to complex networks of interactions that are neither totally regular nor totally random. Partly because of the interactions themselves and partly because of the interaction's topology, complex systems cannot be properly understood by just analyzing their constituent parts.

Humans generate information at an unprecedented pace, with some estimates suggesting that, in a year, we now produce on the order of 10^21 bytes of data, millions of times the amount of information in all the books ever written. Processing this "data deluge", as some have called it, requires new tools and new approaches at the interface of statistics, statistical and machine learning, network theory and statistical physics.

Our goal is to push forward the boundaries of science. We are interested in addressing fundamental questions in all areas of science including natural, social and economic sciences. We put a special emphasis in the development of tools that aid scientific discovery through understanding and quantification of a specific phenomenon. To this end we have assembled a multidisciplinary team and have established solid collaborations with experts in biology, social sciences, ecology and economics.