Temporal stability in predictive process monitoring


Predictive process monitoring is concerned with the analysis of events produced during the execution of a business process in order to predict as early as possible the final outcome of an ongoing case. Traditionally, predictive process monitoring methods are optimized with respect to accuracy. However, in environments where users make decisions and take actions in response to the predictions they receive, it is equally important to optimize the stability of the successive predictions made for each case. To this end, this paper defines a notion of temporal stability for binary classification tasks in predictive process monitoring and evaluates existing methods with respect to both temporal stability and accuracy. We find that methods based on XGBoost and LSTM neural networks exhibit the highest temporal stability. We then show that temporal stability can be enhanced by hyperparameter-optimizing random forests and XGBoost classifiers with respect to inter-run stability. Finally, we show that time series smoothing techniques can further enhance temporal stability at the expense of slightly lower accuracy.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    Inter-run stability refers to the MSPD metric introduced in Liu et al. (2017): \(\textit{MSPD}(f) = 2\mathbb {E}_{x_i}[Var(f(x_i)) - Cov(f_j (x_i), f_k(x_i))],\) where \(\mathbb {E}_{x_i}\) is the expectation over all validation data, f is a mapping from a sample \(x_i\) to a label \(y_i\) on a given run, \(Var(f(x_i))\) is the variance of the predictions of a single data point over the model runs, and \(Cov(f_j (x_i), f_k(x_i))\) is the covariance of predictions of a single data point over two model runs.

  2. 2.

    Production log: https://data.4tu.nl/repository/uuid:68726926-5ac5-4fab-b873-ee76ea412399, other logs: https://data.4tu.nl/repository/collection:event_logs_real.

  3. 3.

    Preprocessed data: https://github.com/irhete/stability-predictive-monitoring.

  4. 4.


  5. 5.


  6. 6.



  1. Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J Mach Learn Res 13:281–305

    MathSciNet  MATH  Google Scholar 

  2. Bousquet O, Elisseeff A (2002) Stability and generalization. J Mach Learn Res 2:499–526

    MathSciNet  MATH  Google Scholar 

  3. Breiman L (1996) Bagging predictors. Mach Learn 24(2):123–140

    MATH  Google Scholar 

  4. Breiman L (2001) Random forests. Mach Learn 45(1):5–32

    Article  MATH  Google Scholar 

  5. Chen T, Guestrin C (2016) XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, ACM, pp 785–794

  6. de Leoni M, van der Aalst WM, Dees M (2016) A general process mining framework for correlating, predicting and clustering dynamic behavior based on event logs. Inf Syst 56:235–257

    Article  Google Scholar 

  7. Di Francescomarino C, Dumas M, Maggi FM, Teinemaa I (2017) Clustering-based predictive process monitoring. IEEE Trans Serv Comput. https://doi.org/10.1109/TSC.2016.2645153

  8. Dumas M, La Rosa M, Mendling J, Reijers HA (2013) Fundamentals of business process management. Springer, Berlin

    Google Scholar 

  9. Elisseeff A, Evgeniou T, Pontil M (2005) Stability of randomized learning algorithms. J Mach Learn Res 6:55–79

    MathSciNet  MATH  Google Scholar 

  10. Evermann J, Rehse JR, Fettke P (2017) Predicting process behaviour using deep learning. Decis Support Syst 100:129–40

    Article  Google Scholar 

  11. Fernández-Delgado M, Cernadas E, Barro S, Amorim D (2014) Do we need hundreds of classifiers to solve real world classification problems. J Mach Learn Res 15(1):3133–3181

    MathSciNet  MATH  Google Scholar 

  12. Guo C, Pleiss G, Sun Y, Weinberger KQ (2017) On calibration of modern neural networks. arXiv preprint arXiv:1706.04599

  13. Lakshmanan GT, Duan S, Keyser PT, Curbera F, Khalaf R (2010) Predictive analytics for semi-structured case oriented business processes. In: International conference on business process management. Springer, Berlin, pp 640–651

  14. Leontjeva A, Conforti R, Di Francescomarino C, Dumas M, Maggi FM (2015) Complex symbolic sequence encodings for predictive monitoring of business processes. In: International conference on business process management. Springer, Berlin, pp 297–313

  15. Lin YF, Chen HH, Tseng VS, Pei J, et al (2015) Reliable early classification on multivariate time series with numerical and categorical attributes. In: PAKDD (1), pp 199–211

  16. Liu CB, Chamberlain BP, Little DA, Cardoso  (2017) Generalising random forest parameter optimisation to include stability and cost. In: Joint European conference on machine learning and knowledge discovery in databases. Springer, Berlin, pp 102–113

  17. Maggi FM, Di Francescomarino C, Dumas M, Ghidini C (2014) Predictive monitoring of business processes. In: International conference on advanced information systems engineering. Springer, Berlin, pp 457–472

  18. Marquez-Chamorro AE, Resinas M, Ruiz-Cortes A (2017) Predictive monitoring of business processes: a survey. IEEE Trans Serv Comput

  19. Metzger A, Leitner P, Ivanovic D, Schmieders E, Franklin R, Carro M, Dustdar S, Pohl K (2015) Comparing and combining predictive business process monitoring techniques. IEEE Trans Syst Man Cybern Syst 45(2):276–290

    Article  Google Scholar 

  20. Mori U, Mendiburu A, Keogh E, Lozano JA (2017) Reliable early classification of time series based on discriminating the classes over time. Data Min Knowl Discov 31(1):233–263

    MathSciNet  Article  Google Scholar 

  21. Niculescu-Mizil A, Caruana R (2005) Predicting good probabilities with supervised learning. In: Proceedings of the 22nd international conference on machine learning, ACM, pp 625–632

  22. Olson RS, La Cava W, Mustahsan Z, Varik A, Moore JH (2018) Data-driven advice for applying machine learning to bioinformatics problems. Pac Symp Biocomput 23:192–203

    Google Scholar 

  23. Osborne J (2013) Dealing with missing or incomplete data: debunking the myth of emptiness. In: Best practices in data cleaning: a complete guide to everything you need to do before and after collecting your data. Sage, Thousand Oaks, pp 105–138

    Google Scholar 

  24. Parrish N, Anderson HS, Gupta MR, Hsiao DY (2013) Classifying with confidence from incomplete information. J Mach Learn Res 14(1):3561–3589

    MathSciNet  MATH  Google Scholar 

  25. Platt J et al (1999) Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. Adv Large Margin Classif 10(3):61–74

    Google Scholar 

  26. Polato M, Sperduti A, Burattin A, de Leoni M (2014) Data-aware remaining time prediction of business process instances. In: International joint conference on IEEE neural networks (IJCNN), pp 816–823

  27. Rogge-Solti A, Weske M (2013) Prediction of remaining service execution time using stochastic petri nets with arbitrary firing delays. In: International conference on service-oriented computing (ICSOC). Springer, Berlin, pp 389–403

  28. Santos T, Kern R (2016) A literature survey of early time series classification and deep learning. In: Proceedings of the 1st international workshop on science, application and methods in industry 4.0 co-located with i-KNOW 2016. CEUR workshop proceedings, vol 1793. CEUR-WS.org

  29. Schafer JL, Graham JW (2002) Missing data: our view of the state of the art. Psychol methods 7(2):147

    Article  Google Scholar 

  30. Senderovich A, Di Francescomarino C, Ghidini C, Jorbina K, Maggi FM (2017) Intra and inter-case features in predictive process monitoring: a tale of two dimensions. In: International conference on business process management. Springer, Berlin, pp 306–323

  31. Tax N, Verenich I, La Rosa M, Dumas M (2017) Predictive business process monitoring with LSTM neural networks. In: International conference on advanced information systems engineering. Springer, Berlin, pp 477–492

  32. Tax N, Verenich I, La Rosa M, Dumas M (2017) Predictive business process monitoring with LSTM neural networks. In: International conference on advanced information systems engineering. Springer, Berlin, pp 477–492

  33. Teinemaa I, Dumas M, La Rosa M, Maggi FM (2017) Outcome-oriented predictive process monitoring: review and benchmark. arXiv preprint arXiv:1707.06766

  34. van der Aalst WM (2016) Process mining: data science in action. Springer, Berlin

    Google Scholar 

  35. van Dongen BF, Crooy RA, van der Aalst WM (2008) Cycle time prediction: when will this case finally be finished? In: OTM confederated international conferences“ on the move to meaningful internet systems”. Springer, pp 319–336

  36. Xing Z, Pei J, Dong G, Yu PS (2008) Mining sequence classifiers for early prediction. In: Proceedings of the 2008 SIAM international conference on data mining, SIAM, pp 644–655

  37. Xing Z, Pei J, Philip SY (2012) Early classification on time series. Knowl Inf Syst 31(1):105–127

    Article  Google Scholar 

Download references


This research was partly funded by the Estonian Research Council (Grant IUT20-55).

Author information



Corresponding author

Correspondence to Irene Teinemaa.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible editors: Jesse Davis, Elisa Fromont, Derek Greene, Björn Bringmann.



See Tables 5, 6, 7, 8, 9, 10 and Figs. 7, 8, 9, 10.

Table 5 Hyperparameters and distributions used in optimization via random search
Table 6 Optimized hyperparameters (RF)
Table 7 Optimized hyperparameters for single classifiers (XGBoost)
Table 8 Optimized hyperparameters for multiclassifiers (XGBoost)
Table 9 Optimized hyperparameters (LSTM)
Table 10 Optimized hyperparameters (combined inter-run stability and AUC)
Fig. 7

Case length histograms for positive and negative classes

Fig. 8

Prediction accuracy on long cases only

Fig. 9

Prediction accuracy on original (not truncated) traces

Fig. 10

Temporal stability on original (not truncated) traces

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Teinemaa, I., Dumas, M., Leontjeva, A. et al. Temporal stability in predictive process monitoring. Data Min Knowl Disc 32, 1306–1338 (2018). https://doi.org/10.1007/s10618-018-0575-9

Download citation


  • Predictive process monitoring
  • Early sequence classification
  • Stability