A Graph-Theoretic Formulation of Exploratory Blockmodeling

We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G\u27 with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G\u27 directly give the blocks and block interactions of the computed blockmodel. We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ? 4

Mining Time-aware Actor-level Evolution Similarity for Link Prediction in Dynamic Network

Topological evolution over time in a dynamic network triggers both the addition and deletion of actors and the links among them. A dynamic network can be represented as a time series of network snapshots where each snapshot represents the state of the network over an interval of time (for example, a minute, hour or day). The duration of each snapshot denotes the temporal scale/sliding window of the dynamic network and all the links within the duration of the window are aggregated together irrespective of their order in time. The inherent trade-off in selecting the timescale in analysing dynamic networks is that choosing a short temporal window may lead to chaotic changes in network topology and measures (for example, the actors’ centrality measures and the average path length); however, choosing a long window may compromise the study and the investigation of network dynamics. Therefore, to facilitate the analysis and understand different patterns of actor-oriented evolutionary aspects, it is necessary to define an optimal window length (temporal duration) with which to sample a dynamic network. In addition to determining the optical temporal duration, another key task for understanding the dynamics of evolving networks is being able to predict the likelihood of future links among pairs of actors given the existing states of link structure at present time. This phenomenon is known as the link prediction problem in network science. Instead of considering a static state of a network where the associated topology does not change, dynamic link prediction attempts to predict emerging links by considering different types of historical/temporal information, for example the different types of temporal evolutions experienced by the actors in a dynamic network due to the topological evolution over time, known as actor dynamicities. Although there has been some success in developing various methodologies and metrics for the purpose of dynamic link prediction, mining actor-oriented evolutions to address this problem has received little attention from the research community. In addition to this, the existing methodologies were developed without considering the sampling window size of the dynamic network, even though the sampling duration has a large impact on mining the network dynamics of an evolutionary network. Therefore, although the principal focus of this thesis is link prediction in dynamic networks, the optimal sampling window determination was also considered

Module Identification for Biological Networks

Advances in high-throughput techniques have enabled researchers to produce large-scale data on molecular interactions. Systematic analysis of these large-scale interactome datasets based on their graph representations has the potential to yield a better understanding of the functional organization of the corresponding biological systems. One way to chart out the underlying cellular functional organization is to identify functional modules in these biological networks. However, there are several challenges of module identification for biological networks. First, different from social and computer networks, molecules work together with different interaction patterns; groups of molecules working together may have different sizes. Second, the degrees of nodes in biological networks obey the power-law distribution, which indicates that there exist many nodes with very low degrees and few nodes with high degrees. Third, molecular interaction data contain a large number of false positives and false negatives. In this dissertation, we propose computational algorithms to overcome those challenges. To identify functional modules based on interaction patterns, we develop efficient algorithms based on the concept of block modeling. We propose a subgradient Frank-Wolfe algorithm with path generation method to identify functional modules and recognize the functional organization of biological networks. Additionally, inspired by random walk on networks, we propose a novel two-hop random walk strategy to detect fine-size functional modules based on interaction patterns. To overcome the degree heterogeneity problem, we propose an algorithm to identify functional modules with the topological structure that is well separated from the rest of the network as well as densely connected. In order to minimize the impact of the existence of noisy interactions in biological networks, we propose methods to detect conserved functional modules for multiple biological networks by integrating the topological and orthology information across different biological networks. For every algorithm we developed, we compare each of them with the state-of-the-art algorithms on several biological networks. The comparison results on the known gold standard biological function annotations show that our methods can enhance the accuracy of predicting protein complexes and protein functions

Knowledge transfer using latent variable models

textIn several applications, scarcity of labeled data is a challenging problem that hinders the predictive capabilities of machine learning algorithms. Additionally, the distribution of the data changes over time, rendering models trained with older data less capable of discovering useful structure from the newly available data. Transfer learning is a convenient framework to overcome such problems where the learning of a model specific to a domain can benefit the learning of other models in other domains through either simultaneous training of domains or sequential transfer of knowledge from one domain to the others. This thesis explores the opportunities of knowledge transfer in the context of a few applications pertaining to object recognition from images, text analysis, network modeling and recommender systems, using probabilistic latent variable models as building blocks. Both simultaneous and sequential knowledge transfer are achieved through the latent variables, either by sharing these across multiple related domains (for simultaneous learning) or by adapting their distributions to fit data from a new domain (for sequential learning).Electrical and Computer Engineerin

Flexible estimation of temporal point processes and graphs

Handling complex data types with spatial structures, temporal dependencies, or discrete values, is generally a challenge in statistics and machine learning. In the recent years, there has been an increasing need of methodological and theoretical work to analyse non-standard data types, for instance, data collected on protein structures, genes interactions, social networks or physical sensors. In this thesis, I will propose a methodology and provide theoretical guarantees for analysing two general types of discrete data emerging from interactive phenomena, namely temporal point processes and graphs. On the one hand, temporal point processes are stochastic processes used to model event data, i.e., data that comes as discrete points in time or space where some phenomenon occurs. Some of the most successful applications of these discrete processes include online messages, financial transactions, earthquake strikes, and neuronal spikes. The popularity of these processes notably comes from their ability to model unobserved interactions and dependencies between temporally and spatially distant events. However, statistical methods for point processes generally rely on estimating a latent, unobserved, stochastic intensity process. In this context, designing flexible models and consistent estimation methods is often a challenging task. On the other hand, graphs are structures made of nodes (or agents) and edges (or links), where an edge represents an interaction or relationship between two nodes. Graphs are ubiquitous to model real-world social, transport, and mobility networks, where edges can correspond to virtual exchanges, physical connections between places, or migrations across geographical areas. Besides, graphs are used to represent correlations and lead-lag relationships between time series, and local dependence between random objects. Graphs are typical examples of non-Euclidean data, where adequate distance measures, similarity functions, and generative models need to be formalised. In the deep learning community, graphs have become particularly popular within the field of geometric deep learning. Structure and dependence can both be modelled by temporal point processes and graphs, although predominantly, the former act on the temporal domain while the latter conceptualise spatial interactions. Nonetheless, some statistical models combine graphs and point processes in order to account for both spatial and temporal dependencies. For instance, temporal point processes have been used to model the birth times of edges and nodes in temporal graphs. Moreover, some multivariate point processes models have a latent graph parameter governing the pairwise causal relationships between the components of the process. In this thesis, I will notably study such a model, called the Hawkes model, as well as graphs evolving in time. This thesis aims at designing inference methods that provide flexibility in the contexts of temporal point processes and graphs. This manuscript is presented in an integrated format, with four main chapters and two appendices. Chapters 2 and 3 are dedicated to the study of Bayesian nonparametric inference methods in the generalised Hawkes point process model. While Chapter 2 provides theoretical guarantees for existing methods, Chapter 3 also proposes, analyses, and evaluates a novel variational Bayes methodology. The other main chapters introduce and study model-free inference approaches for two estimation problems on graphs, namely spectral methods for the signed graph clustering problem in Chapter 4, and a deep learning algorithm for the network change point detection task on temporal graphs in Chapter 5. Additionally, Chapter 1 provides an introduction and background preliminaries on point processes and graphs. Chapter 6 concludes this thesis with a summary and critical thinking on the works in this manuscript, and proposals for future research. Finally, the appendices contain two supplementary papers. The first one, in Appendix A, initiated after the COVID-19 outbreak in March 2020, is an application of a discrete-time Hawkes model to COVID-related deaths counts during the first wave of the pandemic. The second work, in Appendix B, was conducted during an internship at Amazon Research in 2021, and proposes an explainability method for anomaly detection models acting on multivariate time series

Advances in knowledge discovery and data mining Part II

19th Pacific-Asia Conference, PAKDD 2015, Ho Chi Minh City, Vietnam, May 19-22, 2015, Proceedings, Part II</p

Efficient Bayesian active learning and matrix modelling

With the advent of the Internet and growth of storage capabilities, large collections of unlabelled data are now available. However, collecting supervised labels can be costly. Active learning addresses this by selecting, sequentially, only the most useful data in light of the information collected so far. The online nature of such algorithms often necessitates efficient computations. Thus, we present a framework for information theoretic Bayesian active learning, named Bayesian Active Learning by Disagreement, that permits efficient and accurate computations of data utility. Using this framework we develop new techniques for active Gaussian process modelling and adaptive quantum tomography. The latter has been shown, in both simulation and laboratory experiments, to yield faster learning rates than any non-adaptive design. Numerous datasets can be represented as matrices. Bayesian models of matrices are becoming increasingly popular because they can handle noisy or missing elements, and are extensible to different data-types. However, efficient inference is crucial to allow these flexible probabilistic models to scale to large real-world datasets. Binary matrices are a ubiquitous datatype, so we present a stochastic inference algorithm for fast learning in this domain. Preference judgements are a common, implicit source of binary data. We present a hybrid matrix factorization/Gaussian process model for collaborative learning from multiple users' preferences. This model exploits both the structure of the matrix and can incorporate additional covariate information to make accurate predictions. We then combine matrix modelling with active learning and propose a new algorithm for cold-start learning with ordinal data, such as ratings. This algorithm couples Bayesian Active Learning by Disagreement with a heteroscedastic model to handle varying levels of noise. This ordinal matrix model is also used to analyze psychometric questionnaires; we analyze classical assumptions made in psychometrics and show that active learning methods can reduce questionnaire lengths substantially.This PhD was supported by the Google European Doctoral Fellowshi

Structural building blocks in graph data : characterised by hyperbolic communities and uncovered by Boolean tensor clustering

Graph data nowadays easily become so large that it is infeasible to study the underlying structures manually. Thus, computational methods are needed to uncover large-scale structural information. In this thesis, we present methods to understand and summarise large networks. We propose the hyperbolic community model to describe groups of more densely connected nodes within networks using very intuitive parameters. The model accounts for a frequent connectivity pattern in real data: a few community members are highly interconnected; most members mainly have ties to this core. Our model fits real data much better than previously-proposed models. Our corresponding random graph generator, HyGen, creates graphs with realistic intra-community structure. Using the hyperbolic model, we conduct a large-scale study of the temporal evolution of communities on online question–answer sites. We observe that the user activity within a community is constant with respect to its size throughout its lifetime, and a small group of users is responsible for the majority of the social interactions. We propose an approach for Boolean tensor clustering. This special tensor factorisation is restricted to binary data and assumes that one of the tensor directions has only non-overlapping factors. These assumptions – valid for many real-world data, in particular time-evolving networks – enable the use of bitwise operators and lift much of the computational complexity from the task.Netzwerke sind heutzutage oft so groß und unübersichtlich, dass manuelle Analysen nicht reichen, um sie zu verstehen. Um zugrundeliegende Strukturen im großen Maßstab zu identifizieren, bedarf es computergestützter Methoden. Unser Modell für hyperbolische Gemeinschaften beschreibt die innere Struktur eng verknüpfter Knotengruppen in Netzwerken mit sehr eingängigen Parametern. Es basiert auf der Beobachtung, dass oft ein kleiner Teil der Knoten einer Gruppe eng miteinander verknüpft ist und die Mehrheit der Gruppenmitglieder nur Verbindungen zu diesem Zentrum aufweist. Unser Modell bildet echte Daten besser ab als bisherige Modelle. Der entsprechende Zufallsgraphgenerator, HyGen, erzeugt Graphen mit realistischen innergemeinschaftlichen Strukturen. Anhand unseres Modells analysieren wir die Bildung von Gemeinschaften in online Frage-und-Antwort-Netzwerken. Wir beobachten, dass die Aktivität der Mitglieder über die Zeit konstant ist, bezogen auf die Größe der jeweiligen Gemeinschaft. Außerdem ist stets eine kleine Gruppe von Mitgliedern verantwortlich für den Großteil der Aktivität. Wir schlagen eine Methode für Boolesches Tensor Clustering vor. Diese spezielle Tensorfaktorisierung ist beschränkt auf binäre Daten und wir nehmen an, dass es entlang einer Richtung des Tensors keinen nennenswerten Überlapp der Faktoren gibt. Diese Annahmen ermöglichen die Nutzung von Bitoperationen, mindern den Rechenaufwand erheblich und passen gut zu dem, was in echten Daten zu beobachten ist.Max-Planck-Institut für Informati