Trees are useful structures in computing, and useful structures in process mining, particularly for processes which contain other processes, and so can be organised in some hierarchy.

I have two papers (with co-authors) at the International Conference on Process Mining (ICPM) this year, both using process trees to reason about probability in processes.

The first paper gives two new ways to calculate trace probability on process trees, using a weighted extension called Probabilistic Process Trees (PPTs), previously introduced over here. Trace probability is just the chance a particular sequence of events happens in a given process model, and is a necessary input into most stochastic process quality metrics This process tree solution is closed form and within a parameterised approximation bound. A second solution on a kind of weighted stochastic automata is also included, and used to deal with concurrent subtrees. This is Trace Probability Calculation on Probabilistic Process Trees and is being presented at the Stochatics and Uncertainty workshop. This research was with my colleagues Sander Leemans and Moe Wynn, and a pre-print and slides are available.

The second paper, led by Philipp Bär, is about the probability of subprocesses. Specifically, the chance that a subprocess in a process model is skipped given a particular event log. Again, the setting is process trees, but the lovely novel feature that makes this possible is the use of skip alignments. Alignments describe how a trace from a log and a path through a model can differ. In a non-trivial process, the number of such alignments is well known to explode exponentially, with corresponding consequences for computational cost. Skip alignments use a tree structure (itself echoing process trees) to summarise this space of alignments.

In this paper, Skip Probabilities for Subprocesses, skip alignments are associated with probabilities, using both log information and the stochastic language of the model. This allows us to say subprocess B has X chance of being skipped. This work is being presented at the main track of ICPM, and Moe Wynn and Sander Leemans were also part of the authorship team for this nice result. You can find a preprint here.

References

Bär, P., Burke, A.T., Leemans, S.J.J, Wynn, Moe T. (2025). Skip Probabilities for Subprocesses.

Burke, A., Leemans, S. J. J., & Wynn, Moe Thandar. (2021). Discovering Stochastic Process Models By Reduction and Abstraction.

Burke, A.T., Leemans, S.J.J, Wynn, Moe T. (2025). Trace Probability Calculation on Probabilistic Process Trees.