arXiv subjects

Diego Garlaschelli

Publications and source records attributed to Diego Garlaschelli.

At least 91 records · Page 5Linked to original sources

arXiv2017

Reconstruction of multiplex networks with correlated layers

The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is empirically inaccessible, and one has to resort to probabilistic techniques to infer it from limited information. While network reconstruction methods have reached some degree of maturity in the case of single-layer networks (where nodes can be connected only by one type of links), the problem is practically unexplored in the case of multiplex networks, where several interdependent layers, each with a different type of links, coexist. Even the most advanced network reconstruction techniques, if applied to each layer separately, fail in replicating the observed inter-layer dependencies making up the whole coupled multiplex. Here we develop a methodology to reconstruct a class of correlated multiplexes which includes the World Trade Multiplex as a specific example we study in detail. Our method starts from any reconstruction model that successfully reproduces some desired marginal properties, including node strengths and/or node degrees, of each layer separately. It then introduces the minimal dependency structure required to replicate an additional set of higher-order properties that quantify the portion of each node's degree and each node's strength that is shared and/or reciprocated across pairs of layers. These properties are found to provide empirically robust measures of inter-layer coupling. Our method allows joint multi-layer connection probabilities to be reliably reconstructed from marginal ones, effectively bridging the gap between single-layer properties and truly multiplex information.

physics.soc-ph↗

arXiv2017

Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks

Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets is strongly affected by the interconnections among financial institutions. Yet, while the aggregate balance sheets of institutions are publicly disclosed, information on single positions is mostly confidential and, as such, unavailable. Standard approaches to reconstruct the network of financial interconnection produce unrealistically dense topologies, leading to a biased estimation of systemic risk. Moreover, reconstruction techniques are generally designed for monopartite networks of bilateral exposures between financial institutions, thus failing in reproducing bipartite networks of security holdings (\eg, investment portfolios). Here we propose a reconstruction method based on constrained entropy maximization, tailored for bipartite financial networks. Such a procedure enhances the traditional {\em capital-asset pricing model} (CAPM) and allows to reproduce the correct topology of the network. We test this ECAPM method on a dataset, collected by the European Central Bank, of detailed security holdings of European institutional sectors over a period of six years (2009-2015). Our approach outperforms the traditional CAPM and the recently proposed MECAPM both in reproducing the network topology and in estimating systemic risk due to fire-sales spillovers. In general, ECAPM can be applied to the whole class of weighted bipartite networks described by the fitness model.

q-fin.RM↗

arXiv2017

Irreducible network backbones: unbiased graph filtering via maximum entropy

Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in some embedding space. In any real-world network, some links may be reducible, and others irreducible, to such local properties. This dichotomy persists despite the steady increase in data availability and resolution, which actually determines an even stronger need for filtering techniques aimed at discerning essential links from non-essential ones. Here we introduce a rigorous method that, for any desired level of statistical significance, outputs the network backbone that is irreducible to the local properties of nodes, i.e. their degrees and strengths. Unlike previous approaches, our method employs an exact maximum-entropy formulation guaranteeing that the filtered network encodes only the links that cannot be inferred from local information. Extensive empirical analysis confirms that this approach uncovers essential backbones that are otherwise hidden amidst many redundant relationships and inaccessible to other methods. For instance, we retrieve the hub-and-spoke skeleton of the US airport network and many specialised patterns of international trade. Being irreducible to local transportation and economic constraints of supply and demand, these backbones single out genuinely higher-order wiring principles.

physics.soc-ph↗

arXiv2016

Network reconstruction via density sampling

Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to reliably replicate the empirical degree sequence, which is however unknown in many realistic situations. More recently, it has been found that the knowledge of the degree sequence can be replaced by the knowledge of the strength sequence, which is typically accessible, complemented by that of the total number of links, thus considerably relaxing the observational requirements. Here we further relax these requirements and devise a procedure valid when even the the total number of links is unavailable. We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density. We show that the best way of sampling nodes is the random selection scheme, any other procedure being biased towards unrealistically large, or small, link densities. We then introduce our core technique for reconstructing both the topology and the link weights of the unknown network in detail. When tested on real economic and financial data sets, our method achieves a remarkable accuracy and is very robust with respect to the sampled subsets, thus representing a reliable practical tool whenever the available topological information is restricted to small portions of nodes.

physics.soc-ph↗

arXiv2016

ScienceWISE: Topic Modeling over Scientific Literature Networks

We provide an up-to-date view on the knowledge management system ScienceWISE (SW) and address issues related to the automatic assignment of articles to research topics. So far, SW has been proven to be an effective platform for managing large volumes of technical articles by means of ontological concept-based browsing. However, as the publication of research articles accelerates, the expressivity and the richness of the SW ontology turns into a double-edged sword: a more fine-grained characterization of articles is possible, but at the cost of introducing more spurious relations among them. In this context, the challenge of continuously recommending relevant articles to users lies in tackling a network partitioning problem, where nodes represent articles and co-occurring concepts create edges between them. In this paper, we discuss the three research directions we have taken for solving this issue: i) the identification of generic concepts to reinforce inter-article similarities; ii) the adoption of a bipartite network representation to improve scalability; iii) the design of a clustering algorithm to identify concepts for cross-disciplinary articles and obtain fine-grained topics for all articles.

cs.DL↗

arXiv2016

Ensemble nonequivalence in random graphs with modular structure

Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must be met by every graph, soft constraints must be met only on average, subject to maximal entropy. In Squartini et al. (2015) it was shown that ensembles of random graphs are non-equivalent when the degrees of the nodes are constrained, in the sense of a non-zero limiting specific relative entropy as the number of nodes diverges. In that paper, the nodes were placed either on a single layer (uni-partite graphs) or on two layers (bi-partite graphs). In the present paper we consider an arbitrary number of intra-connected and inter-connected layers, thus allowing for modular graphs with a multi-partite, multiplex, block-model or community structure. We give a full classification of ensemble equivalence, proving that breakdown occurs if and only if the number of local constraints (i.e., the number of constrained degrees) is extensive in the number of nodes, irrespective of the layer structure. In addition, we derive a formula for the specific relative entropy and provide an interpretation of this formula in terms of Poissonisation of the degrees.

math.PR↗

arXiv2016

Multiplexity and multireciprocity in directed multiplexes

Real-world multi-layer networks feature nontrivial dependencies among links of different layers. Here we argue that, if links are directed, dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of `multiplexity', there is also a tendency to anti-align as the result of what we call `multireciprocity', i.e. the fact that links in one layer can be reciprocated by \emph{opposite} links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the World Trade Multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is however largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness/complexity metrics.

physics.soc-ph↗

arXiv2016

Ground truth? Concept-based communities versus the external classification of physics manuscripts

Community detection techniques are widely used to infer hidden structures within interconnected systems. Despite demonstrating high accuracy on benchmarks, they reproduce the external classification for many real-world systems with a significant level of discrepancy. A widely accepted reason behind such outcome is the unavoidable loss of non-topological information (such as node attributes) encountered when the original complex system is represented as a network. In this article we emphasize that the observed discrepancies may also be caused by a different reason: the external classification itself. For this end we use scientific publication data which i) exhibit a well defined modular structure and ii) hold an expert-made classification of research articles. Having represented the articles and the extracted scientific concepts both as a bipartite network and as its unipartite projection, we applied modularity optimization to uncover the inner thematic structure. The resulting clusters are shown to partly reflect the author-made classification, although some significant discrepancies are observed. A detailed analysis of these discrepancies shows that they carry essential information about the system, mainly related to the use of similar techniques and methods across different (sub)disciplines, that is otherwise omitted when only the external classification is considered.

cs.DL↗

arXiv2015

The double role of GDP in shaping the structure of the International Trade Network

The International Trade Network (ITN) is the network formed by trade relationships between world countries. The complex structure of the ITN impacts important economic processes such as globalization, competitiveness, and the propagation of instabilities. Modeling the structure of the ITN in terms of simple macroeconomic quantities is therefore of paramount importance. While traditional macroeconomics has mainly used the Gravity Model to characterize the magnitude of trade volumes, modern network theory has predominantly focused on modeling the topology of the ITN. Combining these two complementary approaches is still an open problem. Here we review these approaches and emphasize the double role played by GDP in empirically determining both the existence and the volume of trade linkages. Moreover, we discuss a unified model that exploits these patterns and uses only the GDP as the relevant macroeconomic factor for reproducing both the topology and the link weights of the ITN.

q-fin.GN↗

arXiv2015

Breaking of ensemble equivalence in networks

It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the microcanonical and canonical ensembles are not equivalent have been identified. A complete theory of this intriguing phenomenon is still missing. Here we show that ensemble nonequivalence can manifest itself also in random graphs with topological constraints. We find that, while graphs with a given number of links are ensemble-equivalent, graphs with a given degree sequence are not. This result holds irrespective of whether the energy is nonadditive (as in unipartite graphs) or additive (as in bipartite graphs). In contrast with previous expectations, our results show that: (1) physically, nonequivalence can be induced by an extensive number of local constraints, and not necessarily by long-range interactions or nonadditivity; (2) mathematically, nonquivalence is determined by a different large-deviation behaviour of microcanonical and canonical probabilities for a single microstate, and not necessarily for almost all microstates. The latter criterion, which is entirely local, is not restricted to networks and holds in general.

cond-mat.stat-mech↗

arXiv2015

Systemic risk analysis in reconstructed economic and financial networks

We address a fundamental problem that is systematically encountered when modeling complex systems: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information that can be accessed and, as a consequence, the possibility of correctly estimating the resilience of these systems to events such as financial shocks, crises and cascade failures. Here we present an innovative method to reconstruct the structure of such partially-accessible systems, based on the knowledge of intrinsic node-specific properties and of the number of connections of only a limited subset of nodes. This information is used to calibrate an inference procedure based on fundamental concepts derived from statistical physics, which allows to generate ensembles of directed weighted networks intended to represent the real system, so that the real network properties can be estimated with their average values within the ensemble. Here we test the method both on synthetic and empirical networks, focusing on the properties that are commonly used to measure systemic risk. Indeed, the method shows a remarkable robustness with respect to the limitedness of the information available, thus representing a valuable tool for gaining insights on privacy-protected economic and financial systems.

physics.soc-ph↗

arXiv2015

Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations

The mesoscopic organization of complex systems, from financial markets to the brain, is an intermediate between the microscopic dynamics of individual units (stocks or neurons, in the mentioned cases), and the macroscopic dynamics of the system as a whole. The organization is determined by "communities" of units whose dynamics, represented by time series of activity, is more strongly correlated internally than with the rest of the system. Recent studies have shown that the binary projections of various financial and neural time series exhibit nontrivial dynamical features that resemble those of the original data. This implies that a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. Here, we explore whether the binary signatures of multiple time series can replicate the same complex community organization of the financial market, as the original weighted time series. We adopt a method that has been specifically designed to detect communities from cross-correlation matrices of time series data. Our analysis shows that the simpler binary representation leads to a community structure that is almost identical with that obtained using the full weighted representation. These results confirm that binary projections of financial time series contain significant structural information.

q-fin.ST↗

arXiv2015

Information Recovery In Behavioral Networks

In the context of agent based modeling and network theory, we focus on the problem of recovering behavior-related choice information from origin-destination type data, a topic also known under the name of network tomography. As a basis for predicting agents' choices we emphasize the connection between adaptive intelligent behavior, causal entropy maximization and self-organized behavior in an open dynamic system. We cast this problem in the form of binary and weighted networks and suggest information theoretic entropy-driven methods to recover estimates of the unknown behavioral flow parameters. Our objective is to recover the unknown behavioral values across the ensemble analytically, without explicitly sampling the configuration space. In order to do so, we consider the Cressie-Read family of entropic functionals, enlarging the set of estimators commonly employed to make optimal use of the available information. More specifically, we explicitly work out two cases of particular interest: Shannon functional and the likelihood functional. We then employ them for the analysis of both univariate and bivariate data sets, comparing their accuracy in reproducing the observed trends.

physics.soc-ph↗

arXiv2015

Unbiased sampling of network ensembles

Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the sampling process is unbiased and efficient. The main approaches are microcanonical, i.e. they sample graphs that match the enforced constraints exactly. Unfortunately, when applied to strongly heterogeneous networks (like most real-world examples), the majority of these approaches become biased and/or time-consuming. Moreover, the algorithms defined in the simplest cases, such as binary graphs with given degrees, are not easily generalizable to more complicated ensembles. Here we propose a solution to the problem via the introduction of a "Maximize and Sample" ("Max & Sam" for short) method to correctly sample ensembles of networks where the constraints are `soft', i.e. realized as ensemble averages. Our method is based on exact maximum-entropy distributions and is therefore unbiased by construction, even for strongly heterogeneous networks. It is also more computationally efficient than most microcanonical alternatives. Finally, it works for both binary and weighted networks with a variety of constraints, including combined degree-strength sequences and full reciprocity structure, for which no alternative method exists. Our canonical approach can in principle be turned into an unbiased microcanonical one, via a restriction to the relevant subset. Importantly, the analysis of the fluctuations of the constraints suggests that the microcanonical and canonical versions of all the ensembles considered here are not equivalent. We show various real-world applications and provide a code implementing all our algorithms.

stat.ME↗

arXiv2014

Reconstructing the world trade multiplex: the role of intensive and extensive biases

In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown. However, several studies have proved that real economic networks and multiplexes are topologically very different from configurations inferred only from node strengths. Here we provide a detailed analysis of the World Trade Multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node. We study several temporal snapshots and almost one hundred layers (commodity classes) of the multiplex and find that the observed properties are systematically well reproduced by our model. Our formalism allows us to introduce the (static) concept of extensive and intensive bias, defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights, with respect to a reference case where only strengths are enforced. Our findings complement the existing economic literature on (dynamic) intensive and extensive trade margins. More in general, they show that real-world multiplexes can be strongly shaped by layer-specific local constraints.

q-fin.GN↗

arXiv2014

Community detection for correlation matrices

A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that tends to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.

physics.data-an↗

arXiv2014

Reconstructing topological properties of complex networks using the fitness model

A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this paper we investigate a novel method to reconstruct global topological properties of a complex network starting from limited information. This method uses the knowledge of an intrinsic property of the nodes (indicated as fitness), and the number of connections of only a limited subset of nodes, in order to generate an ensemble of exponential random graphs that are representative of the real systems and that can be used to estimate its topological properties. Here we focus in particular on reconstructing the most basic properties that are commonly used to describe a network: density of links, assortativity, clustering. We test the method on both benchmark synthetic networks and real economic and financial systems, finding a remarkable robustness with respect to the number of nodes used for calibration. The method thus represents a valuable tool for gaining insights on privacy-protected systems.

cs.SI↗

arXiv2014

A GDP-driven model for the binary and weighted structure of the International Trade Network

Recent events such as the global financial crisis have renewed the interest in the topic of economic networks. One of the main channels of shock propagation among countries is the International Trade Network (ITN). Two important models for the ITN structure, the classical gravity model of trade (more popular among economists) and the fitness model (more popular among networks scientists), are both limited to the characterization of only one representation of the ITN. The gravity model satisfactorily predicts the volume of trade between connected countries, but cannot reproduce the observed missing links (i.e. the topology). On the other hand, the fitness model can successfully replicate the topology of the ITN, but cannot predict the volumes. This paper tries to make an important step forward in the unification of those two frameworks, by proposing a new GDP-driven model which can simultaneously reproduce the binary and the weighted properties of the ITN. Specifically, we adopt a maximum-entropy approach where both the degree and the strength of each node is preserved. We then identify strong nonlinear relationships between the GDP and the parameters of the model. This ultimately results in a weighted generalization of the fitness model of trade, where the GDP plays the role of a `macroeconomic fitness' shaping the binary and the weighted structure of the ITN simultaneously. Our model mathematically highlights an important asymmetry in the role of binary and weighted network properties, namely the fact that binary properties can be inferred without the knowledge of weighted ones, while the opposite is not true.

q-fin.GN↗