Probabilistic Trace Alignment
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Presentation of the paper "Probabilistic Trace Alignment" at the 3rd International Conference on Process Mining (ICPM 2021). Paper available here: https://doi.org/10.1109/ICPM53251.2021.9576856 Abstract: Alignments provide sophisticated diagnostics that pinpoint deviations in a trace with respect to a process model. Alignment-based approaches for conformance checking have so far used crisp process models as a reference. Recent probabilistic conformance checking approaches check the degree of conformance of an event log as a whole with respect to a stochastic process model, without providing alignments. For the first time, we introduce a conformance checking approach based on trace alignments using stochastic Workflow nets. This requires to handle the two possibly contrasting forces of the cost of the alignment on the one hand and the likelihood of the model trace with respect to which the alignment is computed on the other.
![Stochastic Petri net with
repeated labels and silent
transitions under “bounded silence”
Bounded
Work
fl
ow
Bounded silence: no loop goes only through silent steps
- at least one visibile transition is needed to indicate
iteration [good for modeling!]](https://image.slidesharecdn.com/icpm2021-probabilistic-trace-alignment-montali-220819225353-55a98fea/85/Probabilistic-Trace-Alignment-26-320.jpg)
Probabilistic Trace Alignment
- 1. ICPM 2021, Eindhoven Probabilistic Trace Alignment Giacomo Bergami, Free University of Bozen-Bolzano Fabrizio M. Maggi, Free University of Bozen-Bolzano Marco Montali, Free University of Bozen-Bolzano Rafael Peñaloza, University of Milano Bicocca
- 3. A process
- 4. A process
- 6. Conformance checking via alignments Match log trace with the “closest” model trace(s) in terms of “moves with disagreement” close accept refuse pay archive Order close, archive
- 7. Conformance checking via alignments Match log trace with the “closest” model trace(s) in terms of “moves with disagreement” close accept refuse pay archive Order close, accept, pay, archive close, refuse, archive close, archive
- 8. Conformance checking via alignments Match log trace with the “closest” model trace(s) in terms of “moves with disagreement” close accept refuse pay archive Order close, archive close accept pay archive close >> >> archive close, accept, pay, archive close, refuse, archive close refuse archive close >> archive d=2 d=1
- 9. Conformance checking via alignments Match log trace with the “closest” model trace(s) in terms of “moves with disagreement” close accept refuse pay archive Order close, archive close accept pay archive close >> >> archive close, accept, pay, archive close, refuse, archive close refuse archive close >> archive d=2 d=1 Non conforming Closest trace: close, refuse, archive
- 10. What if we can “quantify” nondeterminism? Process model describing stochastic behaviors: likely and unlikely to happen! close accept refuse pay archive Order 10% 90%
- 11. What if we can “quantify” nondeterminism? State of the art Process model describing stochastic behaviors: likely and unlikely to happen! close accept refuse pay archive Order 10% 90% Event log Measure of “stochastic language distance” ! in fi nite
- 12. What if we can “quantify” nondeterminism? Our approach: trace by trace… Process model describing stochastic behaviors: likely and unlikely to happen! close accept refuse pay archive Order 10% 90% close, archive
- 13. What if we can “quantify” nondeterminism? Our approach: trace by trace… Process model describing stochastic behaviors: likely and unlikely to happen! close accept refuse pay archive Order 10% 90% close accept pay archive close >> >> archive close, accept, pay, archive close, refuse, archive close refuse archive close >> archive d=2 d=1 P=0.9 P=0.1 close, archive
- 14. What if we can “quantify” nondeterminism? Our approach: trace by trace… Process model describing stochastic behaviors: likely and unlikely to happen! close accept refuse pay archive Order 10% 90% close accept pay archive close >> >> archive close, accept, pay, archive close, refuse, archive close refuse archive close >> archive d=2 d=1 conforming ? Closest trace? P=0.9 P=0.1 close, archive
- 15. Log trace: close, archive Probabilistic trace alignment close accept refuse pay archive Order 10% 90%
- 16. Log trace: close, archive Perfectly aligned Terribly aligned The only possible Impossible Likely Unlikely Model traces Probabilistic trace alignment close accept refuse pay archive Order 10% 90%
- 17. Log trace: close, archive Perfectly aligned Terribly aligned The only possible Impossible Likely Unlikely Model traces Probabilistic trace alignment close accept refuse pay archive Order 10% 90%
- 18. Log trace: close, archive Perfectly aligned Terribly aligned The only possible Impossible Likely Unlikely Model traces Probabilistic trace alignment close accept refuse pay archive Order 10% 90% close, refuse, archive close, accept, pay, archive
- 19. Log trace: close, archive Perfectly aligned Terribly aligned The only possible Impossible Likely Unlikely Model traces Probabilistic trace alignment close accept refuse pay archive Order 10% 90% close, refuse, archive close, accept, pay, archive
- 20. Log trace: close, archive Perfectly aligned Terribly aligned The only possible Impossible Likely Unlikely Model traces Probabilistic trace alignment close accept refuse pay archive Order 10% 90% close, refuse, archive close, accept, pay, archive
- 21. Contributions • Probabilistic trace alignment as a kNN problem: ranked list of top “k” model traces combining alignment distance and probability • Class of “well-behaved” stochastic Petri nets • Pipeline to algorithmically attack the problem • Realization of the pipeline with two ranking strategies: exact and approximated • Implementation and experimental evaluation
- 22. The model: a special type of… Main tasks: (1) calculate the probability of a model trace (2) retrieve all model traces exceeding a minimum probability Stochastic Petri net with repeated labels and silent transitions Main issue: a visible trace may have in fi nitely many supporting runs (due to silent transitions)
- 23. Stochastic Petri net with repeated labels and silent transitions
- 24. Stochastic Petri net with repeated labels and silent transitions Bounded
- 25. Stochastic Petri net with repeated labels and silent transitions Bounded Work fl ow Well-established notion of what a trace/run is. Runs are maximal. Adding elements in a run means “looping more”, which decreases the probability.
- 26. Stochastic Petri net with repeated labels and silent transitions under “bounded silence” Bounded Work fl ow Bounded silence: no loop goes only through silent steps - at least one visibile transition is needed to indicate iteration [good for modeling!]
- 27. Stochastic Petri net with repeated labels and silent transitions under “bounded silence” Bounded Work fl ow Bounded silence: between two consecutive visible steps, there can only be boundedly many invisible ones.
- 28. Good properties of the model 1. Execution semantics captured by a finite-state (stochastic) reachability graph 2. Each trace has finitely many supporting runs 3. Trace probability computable by enumerating those runs and summing up their probabilities 4. Only finitely many trace exceed a strictly positive probability threshold 5. For a log trace, there is a maximal length over model traces after which alignment distance and probability both decrease
- 34. Algorithmic pipeline EXACT ALIGNMENT For each log trace… 1. Invoke an exact aligner on all extracted model traces 2. Rank according to the probability-alignment distance combination
- 35. Algorithmic pipeline APPROXIMATE ALIGNMENT via embeddings 1. Pre-embed all extracted model traces 2. For each log trace… A. Embed the log trace B. Rank by embedding distance
- 36. Algorithmic pipeline APPROXIMATE ALIGNMENT via embeddings 1. Pre-embed all extracted model traces 2. For each log trace… A. Embed the log trace B. Rank by embedding distance
- 37. Algorithmic pipeline APPROXIMATE ALIGNMENT via embeddings 1. Pre-embed all extracted model traces 2. For each log trace… A. Embed the log trace B. Rank by embedding distance
- 38. Algorithmic pipeline APPROXIMATE ALIGNMENT via embeddings 1. Pre-embed all extracted model traces 2. For each log trace… A. Embed the log trace B. Rank by embedding distance
- 39. Experiments (sepsis data set) E ffi ciency and suitability of approximation Results: • Many model traces —> exact approach struggles • Long model traces —> approximation decreases in quality • Current approximation based on bi-grams (embedding in pairs) • N-grams improve approximation on long traces, but require more prerocessing time for building the embedding space
- 40. Conclusions • Stochastic conformance checking at the single trace level • Suitable underlying formal model • Algorithmic pipeline: approximated alignments based on well- established techniques from databases and information retrieval What’s next? • Explore more the formal guarantees of the model • Explore more about models (cf. declarative) • Explore more the approximation spectrum