arXiv subjects

Tiziano Squartini

Publications and source records attributed to Tiziano Squartini.

At least 37 records · Page 2Linked to original sources

arXiv2023

Deterministic, quenched and annealed parameter estimation for heterogeneous network models

At least two, different approaches to define and solve statistical models for the analysis of economic systems exist: the typical, econometric one, interpreting the Gravity Model specification as the expected link weight of an arbitrary probability distribution, and the one rooted into statistical physics, constructing maximum-entropy distributions constrained to satisfy certain network properties. In a couple of recent, companion papers they have been successfully integrated within the framework induced by the constrained minimisation of the Kullback-Leibler divergence: specifically, two, broad classes of models have been devised, i.e. the integrated and the conditional ones, defined by different, probabilistic rules to place links, load them with weights and turn them into proper, econometric prescriptions. Still, the recipes adopted by the two approaches to estimate the parameters entering into the definition of each model differ. In econometrics, a likelihood that decouples the binary and weighted parts of a model, treating a network as deterministic, is typically maximised; to restore its random character, two alternatives exist: either solving the likelihood maximisation on each configuration of the ensemble and taking the average of the parameters afterwards or taking the average of the likelihood function and maximising the latter one. The difference between these approaches lies in the order in which the operations of averaging and maximisation are taken - a difference that is reminiscent of the quenched and annealed ways of averaging out the disorder in spin glasses. The results of the present contribution, devoted to comparing these recipes in the case of continuous, conditional network models, indicate that the annealed estimation recipe represents the best alternative to the deterministic one.

physics.soc-ph↗

arXiv2023

Pattern detection in bipartite networks: a review of terminology, applications and methods

Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices represent distinct entities, they can equivalently be expressed as a pair of bipartite networks that are linked by projection. A variety of diversity statistics and network metrics can then be used to quantify patterns in these matrices and networks. But what should these patterns be compared to? In all of these disciplines, researchers have recognized the necessity of comparing an empirical matrix to a benchmark set of "null" matrices created by randomizing certain elements of the original data. This common need has nevertheless promoted the independent development of methodologies by researchers who come from different backgrounds and use different terminology. Here, we provide a multidisciplinary review of randomization techniques for matrices representing binary, bipartite networks. We aim to translate the concepts from different technical domains into a common language that is accessible to a broad scientific audience. Specifically, after briefly reviewing examples of binary matrix structures across different fields, we introduce the major approaches and common strategies for randomizing these matrices. We then explore the details of and performance of specific techniques, and discuss their limitations and computational challenges. In particular, we focus on the conceptual importance and implementation of structural constraints on the randomization, such as preserving row or columns sums of the original matrix in each of the randomized matrices. Our review serves both as a guide for empiricists in different disciplines, as well as a reference point for researchers working on theoretical and methodological developments in matrix randomization methods.

physics.data-an↗

arXiv2023

Tracing two decades of carbon emissions using a network approach

Carbon emissions are currently attributed to producers although a consumption-aware accounting is advocated. After constructing the Carbon Trade Network, we trace the flow of emissions over the past two decades. Our analysis reveals the presence of an unexpected, positive feedback: despite individual exchanges have become less carbon-intensive, the increase in trading activity has ultimately risen the amount of emissions directed from `net exporters' towards `net importers'. Adopting a consumption-aware accounting would re-distribute responsibility between the two groups, possibly reducing disparities.

physics.soc-ph↗

arXiv2023

Inferring comparative advantage via entropy maximization

We revise the procedure proposed by Balassa to infer comparative advantage, which is a standard tool, in Economics, to analyze specialization (of countries, regions, etc.). Balassa's approach compares the export of a product for each country with what would be expected from a benchmark based on the total volumes of countries and products flows. Based on results in the literature, we show that the implementation of Balassa's idea generates a bias: the prescription of the maximum likelihood used to calculate the parameters of the benchmark model conflicts with the model's definition. Moreover, Balassa's approach does not implement any statistical validation. Hence, we propose an alternative procedure to overcome such a limitation, based upon the framework of entropy maximisation and implementing a proper test of hypothesis: the `key products' of a country are, now, the ones whose production is significantly larger than expected, under a null-model constraining the same amount of information employed by Balassa's approach. What we found is that countries diversification is always observed, regardless of the strictness of the validation procedure. Besides, the ranking of countries' fitness is only partially affected by the details of the validation scheme employed for the analysis while large differences are found to affect the rankings of products Complexities. The routine for implementing the entropy-based filtering procedures employed here is freely available through the official Python Package Index PyPI.

cs.SI↗

arXiv2022

Reconciling econometrics with continuous maximum-entropy network models

In the study of economic networks, econometric approaches interpret the traditional Gravity Model specification as the expected link weight coming from a probability distribution whose functional form can be chosen arbitrarily, while statistical-physics approaches construct maximum-entropy distributions of weighted graphs, constrained to satisfy a given set of measurable network properties. In a recent, companion paper, we integrated the two approaches and applied them to the World Trade Web, i.e. the network of international trade among world countries. While the companion paper dealt only with discrete-valued link weights, the present paper extends the theoretical framework to continuous-valued link weights. In particular, we construct two broad classes of maximum-entropy models, namely the integrated and the conditional ones, defined by different criteria to derive and combine the probabilistic rules for placing links and loading them with weights. In the integrated models, both rules follow from a single, constrained optimization of the continuous Kullback-Leibler divergence; in the conditional models, the two rules are disentangled and the functional form of the weight distribution follows from a conditional, optimization procedure. After deriving the general functional form of the two classes, we turn each of them into a proper family of econometric models via a suitable identification of the econometric function relating the corresponding, expected link weights to macroeconomic factors. After testing the two classes of models on World Trade Web data, we discuss their strengths and weaknesses.

physics.soc-ph↗

arXiv2022

Change my Mind: Data Driven Estimate of Open-Mindedness from Political Discussions

One of the main dimensions characterizing the unfolding of opinion formation processes in social debates is the degree of open-mindedness of the involved population. Opinion dynamic modeling studies have tried to capture such a peculiar expression of individuals' personalities and relate it to emerging phenomena like polarization, radicalization, and ideology fragmentation. However, one of their major limitations lies in the strong assumptions they make on the initial distribution of such characteristics, often fixed so as to satisfy a normality hypothesis. Here we propose a data-driven methodology to estimate users' open-mindedness from online discussion data. Our analysis - focused on the political discussion taking place on Reddit during the first two years of the Trump presidency - unveils the existence of statistically diverse distributions of open-mindedness in annotated sub-populations (i.e., Republicans, Democrats, and Moderates/Neutrals). Moreover, such distributions appear to be stable across time and generated by individual users' behaviors that remain consistent and underdispersed.

cs.SI↗

arXiv2022

The Weighted Bitcoin Lightning Network

The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, and focusing on its weighted, undirected, daily snapshot representation. As the study of the BLN weighted structural properties reveals, it is becoming increasingly 'centralised' at different levels, just as its binary counterpart: 1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths 'enclose' the 51% of the total number of links/total weight is rapidly decreasing; 2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; 3)the weighted BLN topology is becoming increasingly compatible with a core-periphery structure, with the largest nodes 'by strength' constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats - as the ones represented by the so called 'split attacks'.

physics.soc-ph↗

arXiv2022

Gravity models of networks: integrating maximum-entropy and econometric approaches

The World Trade Web (WTW) is the network of international trade relationships among world countries. Characterizing both the local link weights (observed trade volumes) and the global network structure (large-scale topology) of the WTW via a single model is still an open issue. While the traditional Gravity Model (GM) successfully replicates the observed trade volumes by employing macroeconomic properties such as GDP and geographic distance, it, unfortunately, predicts a fully connected network, thus returning a completely unrealistic topology of the WTW. To overcome this problem, two different classes of models have been introduced in econometrics and statistical physics. Econometric approaches interpret the traditional GM as the expected value of a probability distribution that can be chosen arbitrarily and tested against alternative distributions. Statistical physics approaches construct maximum-entropy probability distributions of (weighted) graphs from a chosen set of measurable structural constraints and test distributions resulting from different constraints. Here we compare and integrate the two approaches by considering a class of maximum-entropy models that can incorporate macroeconomic properties used in standard econometric models. We find that the integrated approach achieves a better performance than the purely econometric one. These results suggest that the maximum-entropy construction can serve as a viable econometric framework wherein extensive and intensive margins can be separately controlled for, by combining topological constraints and dyadic macroeconomic variables.

physics.soc-ph↗

arXiv2021

Detecting mesoscale structures by surprise

The importance of identifying the presence of mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to the detection of communities, bipartite and core-periphery structures on binary networks: such an effort has led to the definition of a unified framework based upon the score function called surprise, i.e. a p-value that can be assigned to any given partition of nodes, on both undirected and directed networks. Here, we aim at making a step further, by extending the entire framework to the weighted case: after reviewing the application of the surprise-based formalism to the detection of binary mesoscale structures, we present a suitable generalization of it for detecting weighted mesoscale structures, a topic that has received much less attention. To this aim, we analyze four variants of the surprise; from a technical point of view, this amounts at employing four variants of the hypergeometric distribution: the binomial one for the detection of binary communities, the multinomial one for the detection of binary "bimodular" structures and their negative counterparts for the detection of communities and "bimodular" structures on weighted networks. On top of that, we define two "enhanced" variants of surprise, able to encode both binary and weighted constraints and whose definition rests upon two suitable generalizations of the hypergeometric distribution itself. As a result, we present a general, statistically-grounded approach to detect mesoscale structures on networks via a unified, suprise-based framework. To illustrate the performance of our methods, we, first, test them on a variety of well-established, synthetic benchmarks and, then, apply them to several real-world networks, i.e. social, economic, financial and ecological ones. Moreover, we attach to the paper a Python code implementing all the considered variants of surprise.

physics.soc-ph↗

arXiv2021

Mesoscopic Structure of the Stock Market and Portfolio Optimization

The idiosyncratic (microscopic) and systemic (macroscopic) components of market structure have been shown to be responsible for the departure of the optimal mean-variance allocation from the heuristic `equally-weighted' portfolio. In this paper, we exploit clustering techniques derived from Random Matrix Theory (RMT) to study a third, intermediate (mesoscopic) market structure that turns out to be the most stable over time and provides important practical insights from a portfolio management perspective. First, we illustrate the benefits, in terms of predicted and realized risk profiles, of constructing portfolios by filtering out both random and systemic co-movements from the correlation matrix. Second, we redefine the portfolio optimization problem in terms of stock clusters that emerge after filtering. Finally, we propose a new wealth allocation scheme that attaches equal importance to stocks belonging to the same community and show that it further increases the reliability of the constructed portfolios. Results are robust across different time spans, cross-sectional dimensions and set of constraints defining the optimization problem

q-fin.PM↗

arXiv2021

Reconstructing firm-level interactions: the Dutch input-output network

Recent crises have shown that the knowledge of the structure of input-output networks at the firm level is crucial when studying economic resilience from the microscopic point of view of firms that rewire their connections under supply and demand shocks. Unfortunately, empirical inter-firm network data are rarely accessible and protected by confidentiality. The available methods of network reconstruction from partial information, which have been devised for financial exposures, are inadequate for inter-firm relationships because they treat all pairs of nodes as potentially interacting, thereby overestimating the rewiring capabilities of the system. Here we use two big data sets of transactions in the Netherlands to represent a large portion of the Dutch inter-firm network and document the properties of one of the few analysed networks of this kind. We, then, introduce a generalized maximum-entropy reconstruction method that preserves the production function of each firm in the data, i.e. the input and output flows of each node for each product type. We confirm that the new method becomes increasingly more reliable as a finer product resolution is considered and can therefore be used as a generative model of inter-firm networks with fine production constraints. The likelihood of the model, being related to the entropy, proxies the rewiring capability of the system for a fixed input-output configuration.

physics.soc-ph↗

arXiv2021

Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant patterns in graphs, counting networked configurations with given properties. From a technical point of view, the ERGMs workflow is defined by two subsequent optimization steps: the first one concerns the maximization of Shannon entropy and leads to identify the functional form of the ensemble probability distribution that is maximally non-committal with respect to the missing information; the second one concerns the maximization of the likelihood function induced by this probability distribution and leads to its numerical determination. This second step translates into the resolution of a system of $O(N)$ non-linear, coupled equations (with $N$ being the total number of nodes of the network under analysis), a problem that is affected by three main issues, i.e. accuracy, speed and scalability. The present paper aims at addressing these problems by comparing the performance of three algorithms (i.e. Newton's method, a quasi-Newton method and a recently-proposed fixed-point recipe) in solving several ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion. While Newton's method performs best for relatively little networks, the fixed-point recipe is to be preferred when large configurations are considered, as it ensures convergence to the solution within seconds for networks with hundreds of thousands of nodes (e.g. the Internet, Bitcoin). We attach to the paper a Python code implementing the three aforementioned algorithms on all the ERGMs considered in the present work.

physics.data-an↗

arXiv2021

Analysing Twitter Semantic Networks: the case of 2018 Italian Elections

Social media play a key role in shaping citizens' political opinion. According to the Eurobarometer, the percentage of EU citizens employing online social networks on a daily basis has increased from 18% in 2010 to 48% in 2019. The entwinement between social media and the unfolding of political dynamics has motivated the interest of researchers for the analysis of users online behavior - with particular emphasis on group polarization during debates and echo-chambers formation. In this context, attention has been predominantly directed towards the study of online relations between users while semantic aspects have remained under-explored. In the present paper, we aim at filling this gap by adopting a two-steps approach. First, we identify the discursive communities animating the political debate in the run up of the 2018 Italian Elections as groups of users with a significantly-similar retweeting behavior. Second, we study the semantic mechanisms that shape their internal discussions by monitoring, on a daily basis, the structural evolution of the semantic networks they induce. Above and beyond specifying the semantic peculiarities of the Italian electoral competition, our approach innovates studies of online political discussions in two main ways. On the one hand, it grounds semantic analysis within users' behaviors by implementing a method, rooted in statistical theory, that guarantees that our inference of socio-semantic structures is not biased by any unsupported assumption about missing information; on the other, it is completely automated as it does not rest upon any manual labelling (either based on the users' features or on their sharing patterns). These elements make our method applicable to any Twitter discussion regardless of the language or the topic addressed.

cs.SI↗

arXiv2021

Networked partisanship and framing: a socio-semantic network analysis of the Italian debate on migration

The huge amount of data made available by the massive usage of social media has opened up the unprecedented possibility to carry out a data-driven study of political processes. While particular attention has been paid to phenomena like elite and mass polarization during online debates and echo-chambers formation, the interplay between online partisanship and framing practices, jointly sustaining adversarial dynamics, still remains overlooked. With the present paper, we carry out a socio-semantic analysis of the debate about migration policies observed on the Italian Twittersphere, across the period May-November 2019. As regards the social analysis, our methodology allows us to extract relevant information about the political orientation of the communities of users - hereby called partisan communities - without resorting upon any external information. Remarkably, our community detection technique is sensitive enough to clearly highlight the dynamics characterizing the relationship among different political forces.As regards the semantic analysis, our networks of hashtags display a mesoscale structure organized in a core-periphery fashion, across the entire observation period. Taken altogether, our results point at different, yet overlapping, trajectories of conflict played out using migration issues as a backdrop. A first line opposes communities discussing substantively of migration to communities approaching this issue just to fuel hostility against political opponents; within the second line, a mechanism of distancing between partisan communities reflects shifting political alliances within the governmental coalition. Ultimately, our results contribute to shed light on the complexity of the Italian political context characterized by multiple poles of partisan alignment.

cs.SI↗

arXiv2021

Italian Twitter semantic network during the Covid-19 epidemic

The Covid-19 pandemic has had a deep impact on the lives of the entire world population, inducing a participated societal debate. As in other contexts, the debate has been the subject of several d/misinformation campaigns; in a quite unprecedented fashion, however, the presence of false information has seriously put at risk the public health. In this sense, detecting the presence of malicious narratives and identifying the kinds of users that are more prone to spread them represent the first step to limit the persistence of the former ones. In the present paper we analyse the semantic network observed on Twitter during the first Italian lockdown (induced by the hashtags contained in approximately 1.5 millions tweets published between the 23rd of March 2020 and the 23rd of April 2020) and study the extent to which various discursive communities are exposed to d/misinformation arguments. As observed in other studies, the recovered discursive communities largely overlap with traditional political parties, even if the debated topics concern different facets of the management of the pandemic. Although the themes directly related to d/misinformation are a minority of those discussed within our semantic networks, their popularity is unevenly distributed among the various discursive communities.

cs.SI↗

arXiv2021

Uncovering the mesoscale structure of the credit default swap market to improve portfolio risk modelling

One of the most challenging aspects in the analysis and modelling of financial markets, including Credit Default Swap (CDS) markets, is the presence of an emergent, intermediate level of structure standing in between the microscopic dynamics of individual financial entities and the macroscopic dynamics of the market as a whole. This elusive, mesoscopic level of organisation is often sought for via factor models that ultimately decompose the market according to geographic regions and economic industries. However, at a more general level the presence of mesoscopic structure might be revealed in an entirely data-driven approach, looking for a modular and possibly hierarchical organisation of the empirical correlation matrix between financial time series. The crucial ingredient in such an approach is the definition of an appropriate null model for the correlation matrix. Recent research showed that community detection techniques developed for networks become intrinsically biased when applied to correlation matrices. For this reason, a method based on Random Matrix Theory has been developed, which identifies the optimal hierarchical decomposition of the system into internally correlated and mutually anti-correlated communities. Building upon this technique, here we resolve the mesoscopic structure of the CDS market and identify groups of issuers that cannot be traced back to standard industry/region taxonomies, thereby being inaccessible to standard factor models. We use this decomposition to introduce a novel default risk model that is shown to outperform more traditional alternatives.

q-fin.RM↗

arXiv2021

The Physics of Financial Networks

The field of Financial Networks is a paramount example of the novel applications of Statistical Physics that have made possible by the present data revolution. As the total value of the global financial market has vastly outgrown the value of the real economy, financial institutions on this planet have created a web of interactions whose size and topology calls for a quantitative analysis by means of Complex Networks. Financial Networks are not only a playground for the use of basic tools of statistical physics as ensemble representation and entropy maximization; rather, their particular dynamics and evolution triggered theoretical advancements as the definition of DebtRank to measure the impact and diffusion of shocks in the whole systems. In this review we present the state of the art in this field, starting from the different definitions of financial networks (based either on loans, on assets ownership, on contracts involving several parties -- such as credit default swaps, to multiplex representation when firms are introduced in the game and a link with real economy is drawn) and then discussing the various dynamics of financial contagion as well as applications in financial network inference and validation. We believe that this analysis is particularly timely since financial stability as well as recent innovations in climate finance, once properly analysed and understood in terms of complex network theory, can play a pivotal role in the transformation of our society towards a more sustainable world.

physics.soc-ph↗

arXiv2021

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, we shall focus on the inference methods rooted in statistical physics and information theory. The discussion will be organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections.

physics.soc-ph↗