Link Prediction in Graphs with Autoregressive Features

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into account both sparsity and low rank properties of the matrices. Oracle inequalities are derived and illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank property. The estimate is computed efficiently using proximal methods through a generalized forward-backward agorithm.Comment: NIPS 201

A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market

We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognise preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage.Comment: 19 pages, 6 figure

Efficient algorithms for analyzing large scale network dynamics: Centrality, community and predictability

Large scale networks are an indispensable part of our daily life; be it biological network, smart grids, academic collaboration networks, social networks, vehicular networks, or the networks as part of various smart environments, they are fast becoming ubiquitous. The successful realization of applications and services over them depend on efficient solution to their computational challenges that are compounded with network dynamics. The core challenges underlying large scale networks, for example: determining central (influential) nodes (and edges), interactions and contacts among nodes, are the basis behind the success of applications and services. Though at first glance these challenges seem to be trivial, the network characteristics affect their effective and efficient evaluation strategy. We thus propose to leverage large scale network structural characteristics and temporal dynamics in addressing these core conceptual challenges in this dissertation. We propose a divide and conquer based computationally efficient algorithm that leverages the underlying network community structure for deterministic computation of betweenness centrality indices for all nodes. As an integral part of it, we also propose a computationally efficient agglomerative hierarchical community detection algorithm. Next, we propose a network structure evolution based novel probabilistic link prediction algorithm that predicts set of links occurring over subsequent time periods with higher accuracy. To best capture the evolution process and have higher prediction accuracy we propose multiple time scales with the Markov prediction model. Finally, we propose to capture the multi-periodicity of human mobility pattern with sinusoidal intensity function of a cascaded nonhomogeneous Poisson process, to predict the future contacts over mobile networks. We use real data set and benchmarked approaches to validate the better performance of our proposed approaches --Abstract, page iii

Dynamic network models with applications to finance

This thesis provides new contributions to the field of network models, in two directions. On one hand, we study statistical models of static networks, in particular by contributing to the problem of community detection when link direction is taken into account, thus identifying what are the macroscopic structures of interest for the problem and the conditions for detectability [Wilinski et al., 2019]. Then, we introduce novel statistical models of dynamic networks which are able to capture simultaneously latent dynamics for node-specific characteristics together with link-specific persistence patterns. While the latent dynamics drives the evolution of the network topologies, such as the node degree, i.e. the number of incident links to the node, or the community structure, i.e. how nodes connect each other in forming groups, link persistence preserves the past structure of the network. Within this context, the contribution of the thesis is twofold, both theoretical and empirical [Mazzarisi et al., 2019a, Barucca et al., 2018]. We develop novel methodologies to disentangle the two linkage mechanisms in order to learn correctly both latent variables and static parameters of the models. And we consider also applications to financial data to reveal genuine patterns of persistence, which reflects the role both nodes and links have in the process of network formation and evolution. On the other hand, with a focus on the systemic risk of financial systems, we present a theoretical study of the expectation feedback mechanism which governs the dynamics of a financial network, thus determining its dynamical stability [Mazzarisi et al., 2019b]. Any financial system is an expectation feedback system: the current decisions of financial agents depend on what they expect will occur in the future. Agents\u2019 decisions affect the price dynamics in illiquid markets. Then, when expectations are formed by using models of past observations, the price dynamics itself feeds back on agents\u2019 expectations. This is in effect a feedback dynamics. Interestingly, the process of expectation formation by agents and the price dynamics act on different time scales. In our modeling, it is slow for the agents\u2019 expectations and fast for the price dynamics. Moreover, the agents\u2019 decisions, given the expectations formed on the basis of the random price dynamics, is to some extent deterministic, because they represent the optimal portfolio choice in a heavily regulated market. This separation of time scales is crucial and we are able to characterize analytically the feedback dynamics in the asymptotic limit of one time scale infinitely larger than the other one. Hence, we contribute to the research field of systemic risk with the first analytical proof (to the best of our knowledge) of how expectation feedbacks in relation to the estimation of investments\u2019 risk and dependencies determine the dynamical instability of a financial system. In line with the two research directions, the thesis is divided in two parts. [...