Input Attribution for Statistical Model Checking Using Logistic Regression

  • Jeffery P. HansenEmail author
  • Sagar Chaki
  • Scott Hissam
  • James Edmondson
  • Gabriel A. Moreno
  • David Kyle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10012)


We describe an approach to Statistical Model Checking (SMC) that produces not only an estimate of the probability that specified properties (a.k.a. predicates) are satisfied, but also an “input attribution” for those predicates. We use logistic regression to generate the input attribution as a set of linear and non-linear functions of the inputs that explain conditions under which a predicate is satisfied. These functions provide quantitative insight into factors that influence the predicate outcome. We have implemented our approach on a distributed SMC infrastructure, demeter, that uses Linux Docker containers to isolate simulations (a.k.a. trials) from each other. Currently, demeter is deployed on six 20-core blade servers, and can perform tens of thousands of trials in a few hours. We demonstrate our approach on examples involving robotic agents interacting in a simulated physical environment. Our approach synthesizes input attributions that are both meaningful to the investigator and have predictive value on the predicate outcomes.


Logistic Regression Random Input Initial Distance Polynomial Term Statistical Model Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    A platform for operating docker in production.
  2. 2.
    Dukeman, A., Adams, J.A., Edmondson, J.: Extensible collaborative autonomy using GAMS. In: Proceedings of IRMAS (2016)Google Scholar
  3. 3.
    Chaki, S., Kyle, D.: DMPL: programming and verifying distributed mixed-synchrony and mixed-critical software. Technical report CMU/SEI-2016-TR-005, Software Engineering Institute, Carnegie Mellon University, Pittsburgh (2016).
  4. 4.
    Clarke, E.M., Zuliani, P.: Statistical model checking for cyber-physical systems. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 1–12. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-24372-1_1 CrossRefGoogle Scholar
  5. 5.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of POPL (1977)Google Scholar
  6. 6.
    Cousot, P., Cousot, R., Fähndrich, M., Logozzo, F.: Automatic inference of necessary preconditions. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 128–148. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-35873-9_10 CrossRefGoogle Scholar
  7. 7.
    David, A., Du, D., Guldstrand Larsen, K., Legay, A., Mikučionis, M.: Optimizing control strategy using statistical model checking. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 352–367. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38088-4_24 CrossRefGoogle Scholar
  8. 8.
    David, A., Larsen, K.G., Legay, A., Mikučionis, M., Wang, Z.: Time for statistical model checking of real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 349–355. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22110-1_27 CrossRefGoogle Scholar
  9. 9.
    Rohmer, E., Signgh, S.P.N., Freese, M.: V-REP: a versatile and scalable robot simulation framework. In: Proceedings of IROS (2013)Google Scholar
  10. 10.
    Edmondson, J., Gokhale, A.: Design of a scalable reasoning engine for distributed, real-time and embedded systems. In: Xiong, H., Lee, W.B. (eds.) KSEM 2011. LNCS (LNAI), vol. 7091, pp. 221–232. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-25975-3_20 CrossRefGoogle Scholar
  11. 11.
    Ernst, M.D., Cockrell, J., Griswold, W.G., Notkin, D.: Dynamically discovering likely program invariants to support program evolution. In: Proceedings of ICSE (1999)Google Scholar
  12. 12.
    James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning, 6th edn. Springer, New York (2015)zbMATHGoogle Scholar
  13. 13.
    Hanley, J., McNeil, B.: The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1), 29–36 (1982)CrossRefGoogle Scholar
  14. 14.
    Hosmer, D., Lemeshow, S.: Applied Logistic Regression, 3rd edn. Wiley, Hoboken (2013)CrossRefzbMATHGoogle Scholar
  15. 15.
    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). doi: 10.1007/978-3-642-22110-1_47 CrossRefGoogle Scholar
  16. 16.
    Kyle, D., Hansen, J., Chaki, S.: Statistical model checking of distributed adaptive real-time software. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 269–274. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-23820-3_17 CrossRefGoogle Scholar
  17. 17.
    Merkel, D.: Docker: lightweight Linux containers for consistent development and deployment. Linux J.
  18. 18.
    Moreno, G.A., Cámara, J., Garlan, D., Schmerl, B.: Efficient decision-making under uncertainty for proactive self-adaptation. In: Proceedings of ICAC (2016, to appear)Google Scholar
  19. 19.
    Musliner, D.J., Engstrom, E.: PRISMATIC: unified hierarchical probabilistic verification tool. Technical report AFRL-RZ-WP-TR-2011-2097 (2011)Google Scholar
  20. 20.
    R Development Core Team: R: A Language and Environment for Statistical Computing (2008).
  21. 21.
    Seshachala, S.: Docker vs VMs.
  22. 22.
    Younes, H.L.S.: Ymer: a statistical model checker. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 429–433. Springer, Heidelberg (2005). doi: 10.1007/11513988_43 CrossRefGoogle Scholar
  23. 23.
    Younes, H.L.S.: Verification and planning for stochastic processes with asynchronous events. Ph.D. thesis, CMU, Technical report no. CMU-CS-05-105 (2005)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Jeffery P. Hansen
    • 1
    Email author
  • Sagar Chaki
    • 1
  • Scott Hissam
    • 1
  • James Edmondson
    • 1
  • Gabriel A. Moreno
    • 1
  • David Kyle
    • 1
  1. 1.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations