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Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base…

Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…

A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…

Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we…

A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for…

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…

Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often…

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other.…

We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…

Dynamic Bayesian networks provide a compact and natural representation for complex dynamic systems. However, in many cases, there is no expert available from whom a model can be elicited. Learning provides an alternative approach for…

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…

Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to…

We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…

The structure of complex networks has been of interest in many scientific and engineering disciplines over the decades. A number of studies in the field have been focused on finding the common properties among different kinds of networks…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

Many Bayesian network modelling applications suffer from the issue of data scarcity. Hence the use of expert judgement often becomes necessary to determine the parameters of the conditional probability tables (CPTs) throughout the network.…