Probabilistic Process Discovery with Stochastic Process Trees

TL;DR

The paper addresses stochastic process discovery from event logs, showing that adding stochasticity at the Petri-net level yields ambiguous parameter roles and non-unique parameterization. It introduces stochastic process trees (SPT), a direct probabilistic extension of process trees that assigns probabilities to internal operators, thereby reducing parameter count and clarifying their effects on the stochastic language. The authors formalize the syntax and semantics of SPTs, provide sampling and finite-language approximation methods, and describe an optimization approach using the restricted Earth Mover's Distance to fit SPTs to logs. Preliminary experiments on BPIC13 logs suggest that SPT-based discovery achieves comparable probabilistic fidelity to Petri-net-based methods while using fewer, more interpretable parameters, validating the practicality of the approach and outlining avenues for scalability.

Abstract

In order to obtain a stochastic model that accounts for the stochastic aspects of the dynamics of a business process, usually the following steps are taken. Given an event log, a process tree is obtained through a process discovery algorithm, i.e., a process tree that is aimed at reproducing, as accurately as possible, the language of the log. The process tree is then transformed into a Petri net that generates the same set of sequences as the process tree. In order to capture the frequency of the sequences in the event log, weights are assigned to the transitions of the Petri net, resulting in a stochastic Petri net with a stochastic language in which each sequence is associated with a probability. In this paper we show that this procedure has unfavorable properties. First, the weights assigned to the transitions of the Petri net have an unclear role in the resulting stochastic language. We will show that a weight can have multiple, ambiguous impact on the probability of the sequences generated by the Petri net. Second, a number of different Petri nets with different number of transitions can correspond to the same process tree. This means that the number of parameters (the number of weights) that determines the stochastic language is not well-defined. In order to avoid these ambiguities, in this paper, we propose to add stochasticity directly to process trees. The result is a new formalism, called stochastic process trees, in which the number of parameters and their role in the associated stochastic language is clear and well-defined.