Advertisement

Data-Informed Parameter Synthesis for Population Markov Chains

  • Matej Hajnal
  • Morgane Nouvian
  • David Šafránek
  • Tatjana PetrovEmail author
Conference paper
  • 160 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11705)

Abstract

Stochastic population models are widely used to model phenomena in different areas such as chemical kinetics or collective animal behaviour. Quantitative analysis of stochastic population models easily becomes challenging, due to the combinatorial propagation of dependencies across the population. The complexity becomes especially prominent when model’s parameters are not known and available measurements are limited. In this paper, we illustrate this challenge in a concrete scenario: we assume a simple communication scheme among identical individuals, inspired by how social honeybees emit the alarm pheromone to protect the colony in case of danger. Together, n individuals induce a population Markov chain with n parameters. In addition, we assume to be able to experimentally observe the states only after the steady-state is reached. In order to obtain the parameters of the individual’s behaviour, by utilising the data measurements for population, we combine two existing techniques. First, we use the tools for parameter synthesis for Markov chains with respect to temporal logic properties, and then we employ CEGAR-like reasoning to find the viable parameter space up to desired coverage. We report the performance on a number of synthetic data sets.

References

  1. 1.
    Alistarh, D., Gelashvili, R., Vojnović, M.: Fast and exact majority in population protocols. In: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pp. 47–56. ACM (2015)Google Scholar
  2. 2.
    Aspnes, J., Ruppert, E.: An introduction to population protocols. In: Garbinato, B., Miranda, H., Rodrigues, L. (eds.) Middleware for Network Eccentric and Mobile Applications, pp. 97–120. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-540-89707-1_5CrossRefGoogle Scholar
  3. 3.
    Backenköhler, M., Bortolussi, L., Wolf, V.: Generalized method of moments for stochastic reaction networks in equilibrium. In: Bartocci, E., Lio, P., Paoletti, N. (eds.) CMSB 2016. LNCS, vol. 9859, pp. 15–29. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-45177-0_2CrossRefzbMATHGoogle Scholar
  4. 4.
    Backenkohler, M., Bortolussi, L., Wolf, V.: Moment-based parameter estimation for stochastic reaction networks in equilibrium. IEEE/ACM Trans. Comput. Biol. Bioinf. 15(4), 1180–1192 (2018)CrossRefGoogle Scholar
  5. 5.
    Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: System design of stochastic models using robustness of temporal properties. Theor. Comput. Sci. 587, 3–25 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bortolussi, L., Cardelli, L., Kwiatkowska, M., Laurenti, L.: Approximation of probabilistic reachability for chemical reaction networks using the linear noise approximation. In: Agha, G., Van Houdt, B. (eds.) QEST 2016. LNCS, vol. 9826, pp. 72–88. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-43425-4_5CrossRefzbMATHGoogle Scholar
  7. 7.
    Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: a tutorial. Perform. Eval. 70(5), 317–349 (2013)CrossRefGoogle Scholar
  8. 8.
    Bortolussi, L., Sanguinetti, G.: Learning and designing stochastic processes from logical constraints. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 89–105. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40196-1_7CrossRefGoogle Scholar
  9. 9.
    Bortolussi, L., Silvetti, S.: Bayesian statistical parameter synthesis for linear temporal properties of stochastic models. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 396–413. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-89963-3_23CrossRefGoogle Scholar
  10. 10.
    Brim, L., Češka, M., Dražan, S., Šafránek, D.: Exploring parameter space of stochastic biochemical systems using quantitative model checking. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 107–123. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39799-8_7CrossRefGoogle Scholar
  11. 11.
    Češka, M., Dannenberg, F., Paoletti, N., Kwiatkowska, M., Brim, L.: Precise parameter synthesis for stochastic biochemical systems. Acta Informatica 54(6), 589–623 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Daca, P., Henzinger, T.A., Křetínský, J., Petrov, T.: Faster statistical model checking for unbounded temporal properties. ACM Trans. Comput. Log. (TOCL) 18(2), 12 (2017)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Daws, C.: Symbolic and parametric model checking of discrete-time Markov Chains. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 280–294. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31862-0_21CrossRefzbMATHGoogle Scholar
  14. 14.
    de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78800-3_24CrossRefGoogle Scholar
  15. 15.
    Dehnert, C., et al.: PROPhESY: a PRObabilistic ParamEter SYnthesis tool. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 214–231. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21690-4_13CrossRefGoogle Scholar
  16. 16.
    Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A Storm is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63390-9_31CrossRefGoogle Scholar
  17. 17.
    Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.: Ant Colony Optimization and Swarm Intelligence, vol. 5217. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Kluyver, T., et al.: Jupyter notebooks - a publishing format for reproducible computational workflows. In: Positioning and Power in Academic Publishing: Players, Agents and Agendas, pp. 87–90. IOS Press (2016)Google Scholar
  19. 19.
    Giacobbe, M., Guet, C.C., Gupta, A., Henzinger, T.A., Paixão, T., Petrov, T.: Model checking the evolution of gene regulatory networks. Acta Informatica 54(8), 765–787 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Giardina, I.: Collective behavior in animal groups: theoretical models and empirical studies. HFSP J. 2(4), 205–219 (2008)CrossRefGoogle Scholar
  21. 21.
    Hansen, L.P.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054 (1982)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Hillston, J.: Challenges for quantitative analysis of collective adaptive systems. In: Abadi, M., Lluch Lafuente, A. (eds.) TGC 2013. LNCS, vol. 8358, pp. 14–21. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-05119-2_2CrossRefGoogle Scholar
  23. 23.
    Jansen, N., et al.: Accelerating parametric probabilistic verification. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 404–420. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10696-0_31CrossRefGoogle Scholar
  24. 24.
    Katoen, J.-P.: The probabilistic model checking landscape. In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, pp. 31–45. ACM (2016)Google Scholar
  25. 25.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22110-1_47CrossRefGoogle Scholar
  26. 26.
    Loreti, M., Hillston, J.: Modelling and analysis of collective adaptive systems with CARMA and its tools. In: Bernardo, M., De Nicola, R., Hillston, J. (eds.) SFM 2016. LNCS, vol. 9700, pp. 83–119. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-34096-8_4CrossRefGoogle Scholar
  27. 27.
    Mai, M., et al.: Monitoring pre-seismic activity changes in a domestic animal collective in central Italy. In: EGU General Assembly Conference Abstracts, vol. 20, p. 19348 (2018)Google Scholar
  28. 28.
    Nouvian, M., Reinhard, J., Giurfa, M.: The defensive response of the honeybee Apis mellifera. J. Exp. Biol. 219(22), 3505–3517 (2016)CrossRefGoogle Scholar
  29. 29.
    Daca, P., Henzinger, T.A., Křetínský, J., Petrov, T.: Faster statistical model checking for unbounded temporal properties. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 112–129. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49674-9_7CrossRefGoogle Scholar
  30. 30.
    Polgreen, E., Wijesuriya, V.B., Haesaert, S., Abate, A.: Data-efficient Bayesian verification of parametric Markov Chains. In: Agha, G., Van Houdt, B. (eds.) QEST 2016. LNCS, vol. 9826, pp. 35–51. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-43425-4_3CrossRefzbMATHGoogle Scholar
  31. 31.
    Quatmann, T., Dehnert, C., Jansen, N., Junges, S., Katoen, J.-P.: Parameter synthesis for Markov models: faster than ever. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 50–67. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46520-3_4CrossRefzbMATHGoogle Scholar
  32. 32.
    Schnoerr, D., Sanguinetti, G., Grima, R.: Approximation and inference methods for stochastic biochemical Kinetics–a tutorial review. J. Phys. A: Math. Theor. 50(9), 093001 (2017)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Shorter, J.R., Rueppell, O.: A review on self-destructive defense behaviors in social insects. Insectes Soc. 59(1), 1–10 (2012)CrossRefGoogle Scholar
  34. 34.
    Sokolova, A., de Vink, E.P.: Probabilistic automata: system types, parallel composition and comparison. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 1–43. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24611-4_1CrossRefGoogle Scholar
  35. 35.
    Stoelinga, M.: An introduction to probabilistic automata. Bull. EATCS 78(176–198), 2 (2002)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Česka, M., Šafránek, D., Dražan, S., Brim, L.: Robustness analysis of stochastic biochemical systems. PLoS ONE 9(4), 1–23 (2014)CrossRefGoogle Scholar
  37. 37.
    Wu, S.-H., Smolka, S.A., Stark, E.W.: Composition and behaviors of probabilistic I/O automata. Theor. Comput. Sci. 176(1–2), 1–38 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Matej Hajnal
    • 2
    • 4
  • Morgane Nouvian
    • 1
    • 3
  • David Šafránek
    • 4
  • Tatjana Petrov
    • 2
    • 3
    Email author
  1. 1.Department of BiologyUniversity of KonstanzKonstanzGermany
  2. 2.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany
  3. 3.Centre for the Advanced Study of Collective BehaviourUniversity of KonstanzKonstanzGermany
  4. 4.Systems Biology Laboratory, Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

Personalised recommendations