@article{CecchiniSchelter2018,
  author    = {Cecchini, Gloria and Schelter, Bj{\"o}rn},
  title     = {Analytical approach to network inference},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.022311},
  pages     = {10},
  year      = {2018},
  abstract  = {When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is analytically analyzed. Moreover, an analytic formula of the density of the biased vertex degree distribution is found. In the inverse problem, we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on, e.g., simulation studies.},
  language  = {en}
}
@article{CecchiniThielSchelteretal.2018,
  author    = {Cecchini, Gloria and Thiel, Marco and Schelter, Bj{\"o}rn and Sommerlade, Linda},
  title     = {Improving network inference},
  series = {Journal of neuroscience methods},
  volume    = {307},
  journal   = {Journal of neuroscience methods},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0165-0270},
  doi       = {10.1016/j.jneumeth.2018.06.011},
  pages     = {31 -- 36},
  year      = {2018},
  abstract  = {Background: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. New method: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. Results: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. Comparison with existing methods: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. Conclusions: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.},
  language  = {en}
}
@phdthesis{Cecchini2019,
  author    = {Cecchini, Gloria},
  title     = {Improving network inference by overcoming statistical limitations},
  doi       = {10.25932/publishup-42670},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-426705},
  school      = {Universit{\"a}t Potsdam},
  pages     = {124},
  year      = {2019},
  abstract  = {A reliable inference of networks from data is of key interest in many scientific fields. Several methods have been suggested in the literature to reliably determine links in a network. These techniques rely on statistical methods, typically controlling the number of false positive links, but not considering false negative links. In this thesis new methodologies to improve network inference are suggested. Initial analyses demonstrate the impact of falsepositive and false negative conclusions about the presence or absence of links on the resulting inferred network. Consequently, revealing the importance of making well-considered choices leads to suggest new approaches to enhance existing network reconstruction methods. A simulation study, presented in Chapter 3, shows that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. The existence of type I and type II errors in the reconstructed network, also called biased network, is accepted. Consequently, an analytic method that describes the influence of these two errors on the network structure is explored. As a result of this analysis, an analytic formula of the density of the biased vertex degree distribution is found (Chapter 4). In the inverse problem, the vertex degree distribution of the true underlying network is analytically reconstructed, assuming the probabilities of type I and type II errors. Chapters 4-5 show that the method is robust to incorrect estimates of α and β within reasonable limits. In Chapter 6, an iterative procedure to enhance this method is presented in the case of large errors on the estimates of α and β. The investigations presented so far focus on the influence of false positive and false negative links on the network characteristics. In Chapter 7, the analysis is reversed - the study focuses on the influence of network characteristics on the probability of type I and type II errors, in the case of networks of coupled oscillators. The probabilities of α and β are influenced by the shortest path length and the detour degree, respectively. These results have been used to improve the network reconstruction, when the true underlying network is not known a priori, introducing a novel and advanced concept of threshold.},
  language  = {en}
}