A faster horse on a safer trail: generalized inference for the efficient reconstruction of weighted networks
Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. However, since data about financial linkage...
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| Published in: | New journal of physics Vol. 22; no. 5; pp. 53053 - 53071 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01.05.2020
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| ISSN: | 1367-2630, 1367-2630 |
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| Abstract | Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. 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 were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. 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 safe (i.e. 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 if the bare 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 generalized likelihood among the considered competing models. |
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| AbstractList | Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. 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 were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. 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 safe (i.e. unbiased in the sense of maximum conditional entropy) variants of it. While the one named CReM _A is perfectly general (as a particular case, it can place optimal weights on a network if the bare topology is known), the one named CReM _B 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 CReM _B is faster and reproduces empirical networks with highest generalized likelihood among the considered competing models. Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. 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 were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. 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 safe (i.e. 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 if the bare 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 generalized likelihood among the considered competing models. Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. 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 were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. 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 safe (i.e. unbiased in the sense of maximum conditional entropy) variants of it. While the one named CReM A is perfectly general (as a particular case, it can place optimal weights on a network if the bare topology is known), the one named CReM B 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 CReM B is faster and reproduces empirical networks with highest generalized likelihood among the considered competing models. |
| Author | Squartini, Tiziano Parisi, Federica Garlaschelli, Diego |
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| Cites_doi | 10.1007/978-3-319-47705-3_15 10.1103/PhysRevE.99.030301 10.1088/1367-2630/16/4/043022 10.1103/PhysRevE.84.046118 10.1177/0022002702046005006 10.1007/s10287-013-0168-4 10.1038/srep03357 10.1016/j.physrep.2018.06.008 10.1287/mnsc.2016.2546 10.1088/1367-2630/13/8/083001 10.2307/2525582 10.1038/s42254-018-0002-6 10.1016/j.jfi.2013.08.001 10.1007/s41109-017-0021-8 10.1109/TAC.1974.1100705 10.1080/14697688.2014.968195 10.2139/ssrn.641288 10.1016/j.jfs.2010.12.001 10.1088/1367-2630/17/2/023052 10.1142/S0129183116501485 10.2139/ssrn.3084543 10.1016/j.jfs.2017.05.012 10.1103/PhysRevE.78.015101 10.1088/1742-5468/2012/03/P03011 10.1016/j.jbankfin.2010.09.018 10.1016/j.jedc.2007.01.032 10.1080/14697688.2016.1178855 10.1038/srep15758 10.1103/PhysRevE.92.040802 |
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| StartPage | 53053 |
| SubjectTerms | complex networks Density Entropy entropy maximization Horses network reconstruction Network topologies Optimization Physics Probability distribution functions Reconstruction |
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| Title | A faster horse on a safer trail: generalized inference for the efficient reconstruction of weighted networks |
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| Volume | 22 |
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