Tiago de Paula Peixoto

Associate Professor

Department of Network and Data Science

Central European University

Vienna, Austria

tiago@skewed.de
peixotot@ceu.edu

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Network Modeling, Inference, and Reconstruction

I am an Associate Professor in the Department of Network and Data Science at the Central European University (CEU), Vienna, Austria. I have received my Habilitation in Theoretical Physics at the University of Bremen in 2017. Previously, I have been an Assistant Professor in Applied Mathematics at the University of Bath (2016-2019), External Researcher at the ISI Foundation (2015-2020), and post-doc researcher at the University of Bremen (2011-2016) and Technical University of Darmstadt (2008-2011).

My research lies at the interface between Statistical Physics, Complex Systems, Data Science, Applied Mathematics, and Machine Learning, with a special interest on the theoretical foundations of Network Science.

Networks form the substrate of a dominating class of large-scale complex systems, encompassing socio-economical relations, the human brain, cell metabolism, ecosystems, informational infrastructure, and many more. Being high-dimensional, heterogeneously structured, and often large relational objects, networks require special analytical and methodological frameworks.

I focus on the development of methods to extract scientific understanding from network data, as well as the mathematical modeling of network behavior and evolution. I'm particularly interested in problems of network inference, where meaningful structural and functional patterns cannot be obtained by direct inspection or low-order statistics, and require instead more sophisticated approaches based on large-scale generative models and efficient algorithms derived from them. In more demanding scenarios, the network data is noisy, incomplete, or even completely hidden, leaving its trace only via an observed dynamical behavior — in which case it needs to be fully reconstructed from indirect information.

A central aim of my research is to obtain robust methods and theory that are derived from fundamental principles, while being at the same time algorithmically efficient and interpretable. This is achieved by merging analytical tools and concepts from a variety of disciplines, including Statistical Mechanics, Information Theory, and Bayesian Statistics.

Many of the methods developed in my work are made available as part of the graph-tool library, which is extensively documented. For a practical introduction to many inference and reconstruction algorithms, please refer to the HOWTO.

Research highlights

Inferring modular structures in networks
We develop principled methods to infer the hierarchical, modular structure of networks, based on generative models and Bayesian inference. Our approaches are efficient (scaling up to huge networks) and robust. In particular they are able to avoid both overfitting and underfitting the data. See review [B2] for an introduction, and the HOWTO documentation for graph-tool. See also [24,20,33,23,42,43].
Annotated and attributed networks
Network data are often annotated with weights or covariates on the edges, or metadata on the nodes. We develop inference approaches that are able to leverage this formation to uncover latent, statistically meaningful network structures. Our perspective is that such annotations are just more data — not "ground truth" — and hence are also subject to noise, incompleteness, irrelevance, etc. See [37,31].
Dynamical networks
In many instances, networks are dynamical objects and their structure evolves in time. We develop inference methods that are able to characterize how the large-scale structure dynamically changes. Importantly, instead of imposing a priori characteristic time scales, we extract the relevant scales from data by formulating arbitrary-order dynamical models, within a nonparametric Bayesian inference framework. See [B1,36,34,28].
Uncertain network reconstruction
As is unavoidable in any empirical setting, network data are subject to measurement uncertainties and omissions. However, differently from more established empirical traditions, network data often do not contain reported error assessments of any kind. We develop principled methods of error evaluation and network reconstruction that are able to function even in the demanding scenario where only a single network is observed, and the error magnitudes are unknown. See [39].
Reconstruction from dynamics
Certain networks are impossible, or prohibitively expensive, to be measured directly, and we need to infer their structure from an observed dynamics that takes place on them. We develop Bayesian methods that are able to achieve this reconstruction, and demonstrate how the joint inference of modular network structure with the network itself can significantly improve the reconstruction from indirect dynamics as well, specially when coupled with efficient algorithms. This amounts to a unification of network reconstruction with community detection — two central but traditionally isolated problems in network science, statistics and machine learning. See [40].
Disentangling edge formation mechanisms
Networks are often the result of a variety of different and interdependent generative mechanisms that operate on different scales (e.g. global or local). We are able to show that it is possible, in key cases, to decompose the contributions of each mechanism, based only on the traces they leave behind on the network structure. In particular we show how homophily and triadic closure can be disentangled from each other, given only a single network snapshot. This has important consequences to the interpretation of community detection methods, since the effects of both mechanisms are often conflated. See [50].

Open positions

Interested PhD candidates are encouraged to apply for the "PhD Program in Network Science at CEU".