November 24, 2018
Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system (e.g. the implied level of systemic risk) requires detailed information about the structure of the underlying network. However, since data about financial linkages are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several "horse races" have been conducted to compare the performance of the available financial network reconstruction methods. These comparisons, however, were based on arbitrarily-chosen similarity metrics between the real and the reconstructed network. Here we establish a generalised maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization maximizes the conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved. The resulting approach admits as input any reconstruction method for the purely binary topology and, conditionally on the latter, exploits the available partial information to infer link weights. We find that the most reliable method is obtained by "dressing" the best-performing binary method with an exponential distribution of link weights having a properly density-corrected and link-specific mean value and propose two unbiased (in the sense of maximum conditional entropy) variants of it. While the one named CReMA is perfectly general (as a particular case, it can place optimal weights on a network whose topology is known), the one named CReMB is recommended both in case of full uncertainty about the network topology and if the existence of some links is certain. In these cases, the CReMB is faster and reproduces empirical networks with highest generalised likelihood.
Similar papers 1
June 18, 2018
When studying social, economic and biological systems, one has often access to only limited information about the structure of the underlying networks. An example of paramount importance is provided by financial systems: information on the interconnections between financial institutions is privacy-protected, dramatically reducing the possibility of correctly estimating crucial systemic properties such as the resilience to the propagation of shocks. The need to compensate for ...
July 8, 2013
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate ...
November 27, 2014
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 stru...
September 3, 2019
To capture the systemic complexity of international financial systems, network data is an important prerequisite. However, dyadic data is often not available, raising the need for methods that allow for reconstructing networks based on limited information. In this paper, we are reviewing different methods that are designed for the estimation of matrices from their marginals and potentially exogenous information. This includes a general discussion of the available methodology ...
September 22, 2014
A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to reconstruct the structural properties of complex weighted networks of this kind using only partial information: the total number of nodes and links, and the values of the strength for all nodes. The latter are used as fitness to estimate the u...
October 18, 2016
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, ...
June 24, 2016
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 ...
September 28, 2011
In this paper we estimate the propagation of liquidity shocks through interbank markets when the information about the underlying credit network is incomplete. We show that techniques such as Maximum Entropy currently used to reconstruct credit networks severely underestimate the risk of contagion by assuming a trivial (fully connected) topology, a type of network structure which can be very different from the one empirically observed. We propose an efficient message-passing ...
September 28, 2012
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network...
March 28, 2019
Network (or matrix) reconstruction is a general problem which occurs if the margins of a matrix are given and the matrix entries need to be predicted. In this paper we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on the equivalence we extend the framework of network reconstruction to...