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In this paper, we consider the problem of learning a graph structure from multivariate signals, known as graph signals. Such signals are multivariate observations carrying measurements corresponding to the nodes of an unknown graph, which we desire to infer. They are assumed to enjoy a sparse representation in the graph spectral domain, a feature which is known to carry information related to the cluster structure of a graph. The signals are also assumed to behave smoothly with respect to the underlying graph structure. For the graph learning problem, we propose a new optimization program to learn the Laplacian of this graph and provide two algorithms to solve it, called IGL-3SR and FGL-3SR. Based on a 3-steps alternating procedure, both algorithms rely on standard minimization methods – such as manifold gradient descent or linear programming – and have lower complexity compared to state-of-the-art algorithms. While IGL-3SR ensures convergence, FGL-3SR acts as a relaxation and is significantly faster since its alternating process relies on multiple closed-form solutions. Both algorithms are evaluated on synthetic and real data. They are shown to perform as good or better than their competitors in terms of both numerical performance and scalability. Finally, we present a probabilistic interpretation of the optimization program as a Factor Analysis Model. Keywords: Graph learning, graph Laplacian, non-convex optimization, graph signal processing, sparse coding, clustering.

This work focuses on the estimation of change-points in a time-varying Ising graphical model (outputs −1 or 1) evolving in a piecewise constant fashion. The occurring changes alter the graphical structure of the model, a structure which we also estimate in the present paper. For this purpose, we propose a new optimization program consisting in the minimization of a penalized negative conditional log-likelihood. The objective of the penalization is twofold: it imposes the learned graphs to be sparse and, thanks to a fused-type penalty, it enforces them to evolve piecewise constantly. Using few assumptions, we then give a change-point consistency theorem. Up to our knowledge, we are the first to present such theoretical result in the context of time-varying Ising model. Finally, experimental results on several synthetic examples and a real-world dataset demonstrate the empirical performance of our method.

This work focuses on the estimation of change-points in a time-varying Ising graphical model (outputs −1 or 1) evolving in a piecewise constant fashion. The occurring changes alter the graphical structure of the model, a structure which we also estimate in the present paper. For this purpose, we propose a new optimization program consisting in the minimization of a penalized negative conditional log-likelihood. The objective of the penalization is twofold: it imposes the learned graphs to be sparse and, thanks to a fused-type penalty, it enforces them to evolve piecewise constantly. Using few assumptions, we then give a change-point consistency theorem. Up to our knowledge, we are the first to present such theoretical result in the context of time-varying Ising model. Finally, experimental results on several synthetic examples and a real-world dataset demonstrate the empirical performance of our method.

TUnder the Dynamic Resource Allocation (DRA) model, an administrator has the mission to allocate dynamically a limited budget of resources to the nodes of a network in order to reduce a diffusion process (DP) (e.g. an epidemic). The standard DRA assumes that the administrator has constantly full information and instantaneous access to the entire network. Towards bringing such strategies closer to real-life constraints, we first present the Restricted DRA model extension where, at each intervention round, the access is restricted to only a fraction of the network nodes, called sample. Then, inspired by sequential selection problems such as the well-known Secretary Problem, we propose the Sequential DRA (SDRA) model. Our model introduces a sequential aspect in the decision process over the sample of each round, offering a completely new perspective to the dynamic DP control. Finally, we incorporate several sequential selection algorithms to SDRA control strategies and compare their performance in SIS epidemic simulations.

Falling in Parkinsonian syndromes (PS) is associated with postural instability and consists a common cause of disability among PS patients. Current posturographic practices record the body’s center-of-pressure displacement (statokinesigram) while the patient stands on a force platform. Statokinesigrams, after appropriate signal processing, can offer numerous posturographic features, which however challenges the efforts for valid statistics via standard univariate approaches. In this work, we present the ts-AUC, a non-parametric multivariate two-sample test, which we employ to analyze statokinesigram differences among PS patients that are fallers (PSf) and non-fallers (PSNF). We included 123 PS patients who were classified into PSF or PSNF based on clinical assessment and underwent simple Romberg Test (eyes open/eyes closed). We analyzed posturographic features using both multiple testing with p-value adjustment and the ts-AUC. While the ts-AUC showed significant difference between groups (p-value = 0.01), multiple testing did not show any such difference. Interestingly, significant difference between the two groups was found only using the open-eyes protocol. PSF showed significantly increased antero-posterior movements as well as increased posturographic area, compared to PSNF. Our study demonstrates the superiority of the ts-AUC test compared to standard statistical tools in distinguishing PSF and PSNF in the multidimensional feature space. This result highlights more generally the fact that machine learning-based statistical tests can be seen as a natural extension of classical statistical approaches and should be considered, especially when dealing with multifactorial assessments.

In this paper we consider the task of detecting abnormal communication volume occurring at node-level in communication networks. The signal of the communication activity is modeled by means of a clique stream: each occurring communication event is instantaneous, and activates an undirected subgraph spanning over a set of equally participating nodes. We present a probabilistic framework to model and assess the communication volume observed at any single node. Specifically, we employ non-parametric regression to learn the probability that a node takes part in a certain event knowing the set of other nodes that are involved. On the top of that, we present a concentration inequality around the estimated volume of events in which a node could participate, which in turn allows us to build an efficient and interpretable anomaly scoring function. Finally, the superior performance of the proposed approach is empirically demonstrated in real-world sensor network data, as well as using synthetic communication activity that is in accordance with that latter setting.

In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made while candidates from a finite set are being examined one-by-one. The goal is to assign a limited number of b available jobs to the best possible candidates. Standard SSP variants begin with an empty selection set (cold-starting) and perform the selection process once (single-round), over a single candidate set. In this paper we introduce the Multi-round Sequential Selection Problem (MSSP) which launches a new round of sequential selection each time a new set of candidates becomes available. Each new round has at hand the output of the previous one, i.e. its b selected employees, and tries to update optimally that selection by reassigning each job at most once. Our setting allows changes to take place between two subsequent selection rounds: resignations of previously selected subjects or/and alterations of the quality score across the population. The challenge for a selection strategy is thus to efficiently adapt to such changes. For this novel problem we adopt a cutoff-based approach, where a precise number of candidates should be rejected first before starting to select. We set a rank-based objective of the process over the final job-to-employee assignment and we investigate analytically the optimal cutoff values with respect to the important parameters of the problem. Finally, we present experimental results that compare the efficiency of different selection strategies, as well as their convergence rates towards the optimal solution in the case of stationary score distributions.

This chapter studies information cascades on social networks with a special focus on types of diffusion processes such as rumors and false news. The complex temporal dynamics of information cascades and rapid changes in user interests require flexible mathematical modeling to properly describe the diffusion dynamics. After mentioning the modeling advancements of recent decades, we get to modern models, such as the Information Cascade Model (ICM), that are indeed capable of describing such time-dependent user interests and are thus particularly suited to the analysis of information diffusion. We provide a theoretical analysis of ICM, relating the dynamics of the cascade to structural characteristics of the social network, and then use that analysis to design control policies capable of efficiently reducing the undesired diffusion. The presented framework for activity shaping is generic while enjoying a simple convex relaxation. Finally, we present an algorithm for the control of Continuous-Time Independent Cascades which is evaluated and compared against baseline and state-of-the art approaches through diffusion simulations on real and synthetic social networks.

In this paper we consider the task of the detection of abnormal communication volume, occurring at node-level in a communication network. We model the communication by means of a dynamic graph with edges related to an occurring communication event appearing instantaneously. We propose a statistical model for the communication volume recorded at a single node, in order to detect anomalies. Our approach is evaluated in real-world communication data.

The Information Cascades Model captures dynamical properties of user activity in a social network. In this work, we develop a novel framework for activity shaping under the Continuous-Time Information Cascades Model which allows the administrator for local control actions by allocating targeted resources that can alter the spread of the process. Our framework employs the optimization of the spectral radius of the Hazard matrix, a quantity that has been shown to drive the maximum influence in a network, while enjoying a simple convex relaxation when used to minimize the influence of the cascade. In addition, use-cases such as quarantine and node immunization are discussed to highlight the generality of the proposed activity shaping framework. Finally, we present the NetShape influence minimization method which is compared favorably to baseline and state-of-the-art approaches through simulations on real social networks.

In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Low-Rank Hawkes Process (SLRHP) framework introduces a low-rank approximation of the kernel matrix that allows to perform the nonparametric learning of the d^2 triggering kernels using at most O(ndr^2) operations, where r is the rank of the approximation (r << d, n). This comes as a major improvement to the existing state-of-the-art inference algorithms that are in O(nd^2). Furthermore, the low-rank approximation allows SLRHP to learn representative patterns of interaction between event types, which is usually for the analysis of complex processes in real-world networks.

In this paper, we analyze a large class of dynamic resource allocation (DRA) strategies, named priority planning, that aim to suppress SIS epidemics taking place in a network. This is performed by distributing treatments of limited efficiency to its infected nodes, according to a priority-order precomputed offline. Under this perspective, an efficient DRA strategy for a given network can be designed by learning a proper linear arrangement of its nodes. In our theoretical analysis, we derive upper and lower bounds for the extinction time of the diffusion process that reveal the role of the maxcut of the considered linear arrangement. Accordingly, we highlight that the cutwidth, which is the minimum maxcut of all possible linear arrangements for a network, is a fundamental network property that determines the resource budget required to suppress the epidemic under priority planning. Finally, by making direct use of our theoretical results, we propose a novel and efficient DRA strategy, called maxcut minimization (MCM), which outperforms other competing strategies in our simulations, while offering desirable robustness under various noise profiles.

In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of the kernel matrix that allows to perform the nonparametric learning of the d^2 triggering kernels using at most O(ndr^2) operations, where r is the rank of the approximation (r << d, n). This comes as a major improvement to the existing state-of-the-art inference algorithms that are in O(nd^2). Furthermore, the low-rank approximation allows LRHP to learn representative patterns of interaction between event types, which may be valuable for the analysis of such complex processes in real world datasets. The efficiency and scalability of our approach is illustrated with numerical experiments on simulated as well as real datasets.

In text streams, documents appear over time and their timestamps can be used to improve typical approaches for text representation and clustering. A way to exploit temporal information is through the detection of bursty terms in such streams, i.e. terms that appear in many documents during short time period. Research efforts so far have shown that utilizing the burst information in the text representation can improve the performance of text clustering algorithms. However, most attempts take into account the bursty terms individually, without investigating the relation between them.

In this work, we take advantage of the fact that most of the important documents of a topic are published during the period in which the `main’ topic terms are bursty. Therefore, we focus on both term burstiness and co-burstiness by determining groups of terms that are simultaneously bursty at a time period and also co-occurring in the same documents. Next, the documents that contain co-bursty terms from those groups, are considered as important for the respective topics and are used to construct robust synthetic prototypes following an agglomerative process. These prototypes are finally used to initialize in a deterministic fashion the spherical k-means clustering algorithm. Experimental results validate empirically the quality of the solutions provided by the proposed approach which seems to efficiently overcome the initialization problem of spherical k-means.

This paper investigates the control of a diffusion process by utilizing real-time information. More specifically, we allow the network administrator to adjust the allocation of control resources, a set of treatments that increase the recovery rate of infected nodes, according to the evolution of the diffusion process. We first present a novel framework for describing a large class of dynamic control strategies. These strategies rely on sorting the nodes according to a priority score in order to treat more sensitive regions first. Then, we propose the Largest Reduction in Infectious Edges (LRIE) control strategy which is based on a greedy minimization of the cost associated to the undesired diffusion, and has the benefits of being efficient and easy to implement. Our simulations, which were conducted using a software package that we developed and made available to the community, show that the LRIE strategy substantially outperforms its competitors in a wide range of scenarios.