NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català ADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). 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UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català PhD THESIS Network inference based on Stochastic Block Models: Model extensions, inference approaches and applications Toni Valles` Catala` Copyright © 2016 All Rights Reserved UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català UNIVERSITAT ROVIRA I VIRGILI PhD THESIS Network inference based on Stochastic Block Models: Model extensions, inference approaches and applications Author Toni Valles` Catala` Supervisors Marta Sales-Pardo Roger Guimera` DEPARTMENT OF CHEMICAL ENGINEERING Tarragona, 2016 UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català WE STATE that the present study, entitled “Network inference based on Stochastic Block Models: Model extensions, inference approaches and applications”, presented by Toni Valles` Catala` for the award of the degree of Doctor, has been carried out under our supervision at the Department of Chemical Engineering of this university. Doctoral Thesis Supervisor/s Dr. Roger Guimera` Manrique Dra. Marta Sales Pardo Tarragona, 2nd September 2016 UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català Agra ¨ıments El proces´ de quatre anys dedicats a aquesta tesis ha estat possible gracies` a les per- sones que m’envolten: En primer lloc, voldria agrair als meus supervisors Roger i Marta per confiar en mi i ensenyarme multitud d’eines i d’idees: apart de conceptes tecnics` de f´ısica i diverses metodologies, tambe´ m’han mostrat com treballar rigurosament en ciencia` i com co- municar millor els resultats obtinguts. El seu treball i esforc¸riguros,´ humil i continuat son un exemple de com fer be´ les coses, sempre dedicant gran part del seu temps a la formacio´ de nous doctorats. M’ha encantat formar part del grup SEES Lab, on agraeixo a tots i cadascun dels seus membres, sense ells la feina s’hauria tornat mes´ feixuga. A Nuria,´ Arnau, Francesco, Manu, Toni Aguilar, Toni,˜ Oriol, Marc, Pedro i Sergio. Les nostres discus- sions sobre tot tipus de temes, tant cient´ıfics com intrascendentals, m’han forjat una millor cultura i m’han plantejat preguntes des d’altres punts de vista. Dins d’aquest grup es´ facil` venir a treballar cada mat´ı, on els companys de feina es transformen paulativament en amics. Tambe´ agra¨ır a membres d’altres labs, que han contribu¨ıt en aquest ambient dins de la universitat (Janire, Joan, Angel,` Patricia, Carmen, Dani, Car- los, Victor, Alberto, Yonhara, Judith, Noelia, Sandra). Moltes gracies` a Tiago i Borja per les seves enriquidores col·laboracions, demostrant que la distancia` no impedeix un bon intercanvi d’idees. Tambe´ voldria agra¨ır a totes les persones que m’he anat trobant en congressos i escoles d’estiu. Pol, Oleguer, Mario, Guille, Fede, Massimo, Emmanuelle, Manlio, Manu, Bruno Pace, Bruno Medeiros, Mika, Milo, Marc Sun˜e.´ Les intenses jornades d’interessants xerrades necessiten l’oxigen que ens proporcionem entre companys du- rant els ’coffee breaks’. Per acabar, res del que mai pugui fer no seria possible sense tot el que els meus pares i familia m’han donat. Ells han permes la meva formacio professional i personal UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català 8 per poder optar a fer un doctorat sense oblidar els nostres humils principis. En especial, mai agra¨ıre´ prou tot el que l’Alba fa per mi, dia a dia, amb la enorme paciencia` que comporta escoltar xerrades sobre xarxes i conviure amb algu´ que escriu una tesis. UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català Summary Introduction The development of tools for the analysis of real-world complex networks has signif- icantly advanced our understanding of complex systems in fields as diverse as molec- ular and cell biology [6], neuroscience [11], biomedicine [5, 14], ecology [100, 85], economics [92], anatomy [23] and sociology [9]. One of the main successes of the complex networks approach has been to unravel the relationship between the modular organization of interactions within a complex system [66], and the function and tempo- ral evolution of the system [37, 4, 42, 2]. As a result, a large body of research has been devoted to the detection of the modular structure (or community structure) of complex networks, that is, to the division (partition) of the nodes of the network into densely connected subgroups [28]. Stochastic block models (SBMs) [105, 46, 70] are a class of probabilistic genera- tive network models that provide a more general description of the large-scale structure of real-world networks than modular models. In SBMs, nodes are assumed to belong to groups and connect to each other with probabilities that depend only on their group memberships. The simple mathematical form of SBMs has enabled not only the iden- tification of generalized community structures in networks [70, 50, 18, 91, 74, 76, 75, 56, 3, 108], but also to make network inference a predictive tool to detect missing and spurious links in empirical network data [44], to predict human decisions [41, 39] and the appearance of conflict in work teams [86], and for the identification of unknown interactions between drugs [45]. While these approaches have pushed forward our understanding of complex net- work structure, there are some limitations: (i) it is not clear which inference methodol- ogy yields better predictions, (ii) they rely on the premise that there is a single mecha- nism that describes the connectivity of the network. The goal of this thesis is to develop novel inference approaches that will improve our understanding of complex systems, decide which inference models to use and apply it to real world problems. UNIVERSITAT ROVIRA I VIRGILI NETWORK INFERENCE BASED ON STOCHASTIC BLOCK MODELS: MODEL EXTENSIONS, INFERENCE APPROACHES AND APPLICATIONS Toni Vallès Català 10 Summary Approaches to network inference with stochastic block models The reliability of missing links is the likelihood that a link exists on a given network, it O O RM dM p(Aij =1|M) p(A |M) p(M) can be compute by p(Aij = 1|A ) = O [44], given an RM dM p(A |M) p(M) O observed network A with an adjacency matrix Aij and integrating over all the family of models M.