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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 AND INFERENCE


SEPARATING STRUCTURE FROM STATISTICAL NOISE IN COMPLEX SYSTEMS

Networks delineate the constituent interactions of a broad range of large-scale
complex systems. They are essential to describe socio-economical relations, the
human brain, cell metabolism, ecosystems, epidemic spreading, informational
infrastructure, transportation systems, and many more.

The structure of these network systems is typically large and heterogeneous.
Network theory offers a wide ranging foundation to untangle such intricate
systems, potentially allowing us to predict and control their behavior, as well
as to provide scientific explanations.

A significant obstacle for the comprehension of such high-dimensional relational
objects lies in discerning between signal and randomness. It is crucial to
identify which aspects of these systems arise from random stochastic
fluctuations and which convey valuable information about an underlying
phenomenon. This is a multifaceted problem that often defies intuition, and lies
at the heart of any data-driven analysis.




These three adjacency matrices correspond to the same random graph; the only
difference between them is how the nodes are ordered. Each ordering reveals a
nontrivial—and seemingly compelling—mixing pattern between the nodes. However,
since the graph is completely random, all these patterns are mere statistical
illusions, dredged out of pure randomness, and therefore overfit the data.
Widespread methods of network data analysis cannot distinguish these spurious
patterns from statistically significant ones, posing a significant risk to their
application. (Reload this page to see how many different patterns can be found
in random graphs!)

In our group, we focus on the development of principled and trustworthy methods
to extract scientific understanding from network data, as well as the
mathematical modeling of network behavior and evolution.

Our methods are designed to be robust against overfitting, and to be
algorithmically efficient. This is achieved by merging analytical tools and
concepts from a variety of disciplines, including Information Theory, Bayesian
Statistics, and Statistical Mechanics.

We're 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, but nonetheless ubiquitous scenarios, the network data are
noisy, incomplete, or even completely hidden, leaving their trace only via an
observed dynamical behavior—in which case the network needs to be fully
reconstructed from indirect information.

Most of the methods developed in our group 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.


ABOUT

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).

The research of my group lies at the interface between Statistical Physics,
Complex Systems, Data Science, Applied Mathematics, and Machine Learning, with a
special interest in the methodological foundations of Network Science.


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".