Maximum Entropy Distributions with Applications to Graph Simulation

Published Online:https://doi.org/10.1287/opre.2022.2323

References

  • Ahn D, Kim KK (2018) Efficient simulation for expectations over the union of half-spaces. ACM Trans. Modeling Comput. Simululation 28(3):23.CrossrefGoogle Scholar
  • Aigner M, Triesch E (1994) Realizability and uniqueness in graphs. Discrete Math. 136(1):3–20.CrossrefGoogle Scholar
  • Anand K, van Lelyveld I, Banai Á, Friedrich S, Garratt R, Hałaj G, Fique J, et al. (2018) The missing links: A global study on uncovering financial network structures from partial data. J. Financial Stability 35:107–119.CrossrefGoogle Scholar
  • Avellaneda M, Buff R, Friedman C, Grandchamp N, Kruk L, Newman J (2000) Weighted Monte Carlo: A new technique for calibrating asset-pricing models. Spigler R, ed. Applied and Industrial Mathematics, Venice—2 (Springer, Berlin), 1–31.CrossrefGoogle Scholar
  • Barvinok A (2010) On the number of matrices and a random matrix with prescribed row and column sums and 0–1 entries. Adv. Math. 224(1):316–339.CrossrefGoogle Scholar
  • Bertsimas D, Tsitsiklis JN (1997) Introduction to Linear Optimization (Athena Scientific, Belmont, MA).Google Scholar
  • Bianconi G (2009) Entropy of network ensembles. Phys. Rev. E 79(3):036114.CrossrefGoogle Scholar
  • Blanchet JH (2009) Efficient importance sampling for binary contingency tables. Ann. Appl. Probability 19(3):949–982.CrossrefGoogle Scholar
  • Blitzstein J, Diaconis P (2011) A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Internet Math. 6(4):489–522.CrossrefGoogle Scholar
  • Britton T, Deijfen M, Martin-Löf A (2006) Generating simple random graphs with prescribed degree distribution. J. Statist. Phys. 124:1377–1397.CrossrefGoogle Scholar
  • Brown LD (1986) Fundamentals of statistical exponential families with applications in statistical decision theory. Lecture Notes-Monograph Series (Institute of Mathematical Statistics, Hayward, CA), 9:i–279.Google Scholar
  • Burstein D, Rubin J (2017) Sufficient conditions for graphicality of bidegree sequences. SIAM J. Discrete Math. 31(1):50–62.CrossrefGoogle Scholar
  • Chatterjee S, Diaconis P (2018) The sample size required in importance sampling. Ann. Appl. Probability 28(2):1099–1135.CrossrefGoogle Scholar
  • Chen N, Olvera-Cravioto M (2013) Directed random graphs with given degree distributions. Stochastic Systems 3(1):147–186.LinkGoogle Scholar
  • Chen Y, Diaconis P, Holmes SP, Liu JS (2005) Sequential Monte Carlo methods for statistical analysis of tables. J. Amer. Statist. Assoc. 100(469):109–120.CrossrefGoogle Scholar
  • Cover TM, Thomas JA (2006) Elements of Information Theory, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • Csiszar I (1975) I-divergence geometry of probability distributions and minimization problems. Ann. Probability 3(1):146–158.CrossrefGoogle Scholar
  • Csiszar I, Matus F (2001) Convex cores of measures on R d. Studia Sci. Math. Hungary 38(1–4):177–190.Google Scholar
  • Degryse H, Nguyen G (2007) Interbank exposures: An empirical examination of contagion risk in the Belgian banking system. Internat. J. Central Bank 3(2):123–171.Google Scholar
  • Dembo A, Montanari A (2010) Gibbs measures and phase transitions on sparse random graphs. Brazilian J. Probability Statist. 24(2):137–211.CrossrefGoogle Scholar
  • Desmarais BA, Cranmer SJ (2012) Statistical inference for valued-edge networks: The generalized exponential random graph model. PLoS One 7(1):1–12.CrossrefGoogle Scholar
  • Fishman G (1996) Monte Carlo (Springer Science & Business Media, New York).CrossrefGoogle Scholar
  • Fosdick BK, Larremore DB, Nishimura J, Ugander J (2018) Configuring random graph models with fixed degree sequences. SIAM Rev. 60(2):315–355.CrossrefGoogle Scholar
  • Gandy A, Veraart LA (2016) A Bayesian methodology for systemic risk assessment in financial networks. Management Sci. 63(12):4428–4446.LinkGoogle Scholar
  • Garlaschelli D, Loffredo MI (2008) Maximum likelihood: Extracting unbiased information from complex networks. Phys. Rev. 78(1):015101.Google Scholar
  • Geyer C, Meeden G (2013) Asymptotics for constrained Dirichlet distributions. Bayesian Anal. 8(1):89–110.CrossrefGoogle Scholar
  • Glasserman P, Lelo de Larrea E (2018) Simulation of bipartite or directed graphs with prescribed degree sequences using maximum entropy probabilities. Proc. Winter Simulation Conf. (IEEE, Piscataway, NJ), 1658–1669.Google Scholar
  • Glasserman P, Young HP (2016) Contagion in financial networks. J. Econom. Literature 54(3):779–831.CrossrefGoogle Scholar
  • Glasserman P, Yu B (2005) Large sample properties of weighted Monte Carlo estimators. Oper. Res. 53(2):298–312.LinkGoogle Scholar
  • Greenhill C, McKay BD (2009) Random dense bipartite graphs and directed graphs with specified degrees. Random Structures Algorithms 35(2):222–249.CrossrefGoogle Scholar
  • Hamilton WL, Ying R, Leskovec J (2017) Representation learning on graphs: Methods and applications. Bulletin of the Committee on Data Engineering (IEEE Computer Society, Washington, DC), 40(3):52–74.Google Scholar
  • Holland PW, Leinhardt S (1981) An exponential family of probability distributions for directed graphs. J. Amer. Statist. Assoc. 76(373):33–50.CrossrefGoogle Scholar
  • Kleitman DJ, Wang DL (1973) Algorithms for constructing graphs and digraphs with given valences and factors. Discrete Math. 6(1):79–88.CrossrefGoogle Scholar
  • Lenstra HW (1983) Integer programming with a fixed number of variables. Math. OR 8(4):538–548.LinkGoogle Scholar
  • Liao Y, Weng Y, Wu M, Rajagopal R (2015) Distribution grid topology reconstruction: An information theoretic approach. Proc. North American Power Sympos. (IEEE, Piscataway, NJ), 1–6.Google Scholar
  • Papadimitriou CH, Steiglitz K (1998) Combinatorial Optimization: Algorithms and Complexity (Dover Publications, Mineola, NY).Google Scholar
  • Park J, Newman ME (2004) Statistical mechanics of networks. Phys. Rev. E 70(6):066117.CrossrefGoogle Scholar
  • Patefield W (1981) Algorithm AS 159: An efficient method of generating random R × C tables with given row and column totals. J. Royal Statist. Soc. Ser. C Appl. Statist. 30(1):91–97.Google Scholar
  • Robins G, Snijders T, Wang P, Handcock M, Pattison P (2007) Recent developments in exponential random graph (p*) models for social networks. Soc. Networks 29(2):192–215.CrossrefGoogle Scholar
  • Rubinstein RY, Kroese DP (2013) The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning (Springer Science & Business Media, New York).Google Scholar
  • Saracco F, Di Clemente R, Gabrielli A, Squartini T (2015) Randomizing bipartite networks: The case of the World Trade Web. Sci. Rep. 5:10595.CrossrefGoogle Scholar
  • Squartini T, Garlaschelli D (2011) Analytical maximum-likelihood method to detect patterns in real networks. New J. Phys. 13(8):083001.CrossrefGoogle Scholar
  • Squartini T, Garlaschelli D (2017) Maximum-Entropy Networks: Pattern Detection, Network Reconstruction and Graph Combinatorics (Springer, Berlin).CrossrefGoogle Scholar
  • Szechtman R (2006) A Hilbert space approach to variance reduction. Handbook Oper. Res. Management Sci. 13:259–289.Google Scholar
  • Upper C, Worms A (2004) Estimating bilateral exposures in the German interbank market: Is there a danger of contagion? Eur. Econom. Rev. 48(4):827–849.CrossrefGoogle Scholar
  • Wang G (2020) A fast MCMC algorithm for the uniform sampling of binary matrices with fixed margins. Electron. J. Statist. 14(1):1690–1706.CrossrefGoogle Scholar
  • Wormald N (1999) Models of random regular graphs. London Mathematical Society Lecture Note Series, vol. 267 (Cambridge University Press, Cambridge, UK), 239–298.CrossrefGoogle Scholar
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