Non-parametric Bayesian modeling of complex networks

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model's fit and predictive performance. We explain how advanced non-parametric models for complex networks can be derived and point out relevant literature

A Group-Based Yule Model for Bipartite Author-Paper Networks

This paper presents a novel model for author-paper networks, which is based on the assumption that authors are organized into groups and that, for each research topic, the number of papers published by a group is based on a success-breeds-success model. Collaboration between groups is modeled as random invitations from a group to an outside member. To analyze the model, a number of different metrics that can be obtained in author-paper networks were extracted. A simulation example shows that this model can effectively mimic the behavior of a real-world author-paper network, extracted from a collection of 900 journal papers in the field of complex networks.Comment: 13 pages (preprint format), 7 figure

Nested structure acquired through simple evolutionary process

Nested structure, which is non-random, controls cooperation dynamics and biodiversity in plant-animal mutualistic networks. This structural pattern has been explained in a static (non-growth) network models. However, evolutionary processes might also influence the formation of such a structural pattern. We thereby propose an evolving network model for plant-animal interactions and show that non-random patterns such as nested structure and heterogeneous connectivity are both qualitatively and quantitatively predicted through simple evolutionary processes. This finding implies that network models can be simplified by considering evolutionary processes, and also that another explanation exists for the emergence of non-random patterns and might provide more comprehensible insights into the formation of plant-animal mutualistic networks from the evolutionary perspective.Comment: 12 pages, 4 figure

Statistical inference in bipartite networks applied to social dilemmas and human microbial systems

La predicció de ‘links’ o enllaços en xarxes complexes és un problema de molta importància, degut a la utilitat pràctica que implica. La capacitat de predir enllaços correctament en una xarxa és, però, també una conseqüència directa de la comprensió del funcionament i de les dinàmiques del sistema que s’estudia. En aquesta tesi doctoral, s’explora el problema de la predicció interpretable d’enllaços en xarxes complexes. En particular, l’anàlisi es centra en xarxes bipartides amb diferents tipus d’enllaços, degut a la seva presència en multitud de sistemes socials i naturals, així com a la seva capacitat d’analitzar diferents tipus d’interaccions. En aquest sentit, es presenta una família de models amb els quals és possible fer prediccions interpretables d’enllaços en aquest tipus de xarxes. Posteriorment, aquests models s’apliquen a dos problemes de diferents disciplines. En primer lloc, considerem un experiment social en el que un grup nombrós de persones pren decisions estratègiques en el context de la teoria de jocs. Observem que és possible agrupar les persones segons el seu comportament coŀlectiu a l’hora de prendre decisions. En funció d’aquests grups, podem predir correctament aproximadament el 75% de les decisions. En segon lloc, s’estudia un problema de microbiota intestinal humana en el que tenim mostres microbials d’un nombre elevat de pacients. De manera anàloga al problema anterior, intentem trobar grups de pacients basant-nos en les similituds del seus perfils microbials. D’acord amb aquests grups, aconseguim predir al voltant d’un 80% de les abundàncies. En conclusió, es demostra que és possible aplicar aquesta família de mètodes a problemes molt diferents, de tal manera que podem construir models predictius i interpretables, basats en la capacitat d’identificar grups o comunitats de nodes, així com de monitoritzar les interaccions entre aquestes comunitats.La predicción de ‘links’ o enlaces en redes complejas es un problema de suma importancia debido a la utilidad práctica que comporta. Sin embargo, la capacidad de predecir links correctamente en una red, es también la consecuencia de la comprensión del funcionamiento y las dinámicas del sistema que se estudia. En esta tesis, exploramos el problema de la predicción interpretable de links en redes complejas. En particular, nos centramos en redes bipartidas con varios tipos de links, debido a su ubicuidad en multitud de sistemas sociales y naturales, así como a la riqueza formal que aportan a nivel de las interacciones. A tal efecto, presentamos una familia de modelos con los que es posible hacer predicciones de links interpretables en dichas redes y la aplicamos a dos problemas de diferentes campos. En primer lugar, consideramos un experimento social en el que un grupo numeroso de personas toma decisiones estratégicas en el contexto de la teoría de juegos. Observamos que podemos agrupar a las personas por su comportamiento colectivo a la hora de tomar decisiones y que, en base a esos grupos, podemos predecir correctamente el 75% de las decisiones aproximadamente. En segundo lugar, estudiamos un problema de microbiota intestinal humana en el que tenemos muestras microbiales de un número elevado de pacientes. De manera análoga al problema anterior, intentamos encontrar grupos de pacientes por las similitudes en sus perfiles microbiales y, sobre esa base, predecir las abundancias de las diferentes especies de microbios. Conseguimos predecir aproximadamente un 80% de las abundancias. En definitiva, demostramos que es posible aplicar nuestros métodos a problemas muy diferentes, de tal manera que podemos construir modelos predictivos e interpretables, basados en la capacidad de identificar grupos o comunidades de nodos, así como de monitorizar las interacciones entre dichas comunidades.Link prediction in complex networks is a very important problem due to its practical importance. However, the ability of predicting links successfully arises naturally from a good understanding of the functioning and the dynamics of the system under study. In this thesis, we explore the problem of interpretable link prediction in complex networks. In particular, we focus on multilink bipartite networks; first, because bipartite networks are ubiquitous in many natural and social systems and second, because the existence of multiple links allows us to analyze different types of interactions. To that end, we present a family of models that can make interpretable link prediction in this kind of networks and we apply them to two different problems. In the first problem, we consider a social experiment in which a large group of people make strategic decisions in a game theoretical context. We observe that it is possible to find groups of people according to their collective strategic behaviors (i.e., how do they make decisions) and that it is possible to make link prediction upon those groups. In our case we can successfully predict around 75% of the decisions. The second problem is a human microbiology one. We have data on gut microbiome samples from a large number of patients. In a similar fashion, we look for groups of patients according to similarities in their microbial profiles. We then make predictions of microbial abundances using that group structure with an approximately 80% accuracy rate. In conclusion, we show that it is possible to implement our methods to problems that are very different in their nature, so that we can build predictive and interpretable models that work on the ability to identify groups or communities of nodes and track the interactions among those communities