Probabilistic Process Discovery with Stochastic Process Trees

2025-04-08

AI Summary

Existing approaches for mapping event logs to stochastic Petri nets suffer from ambiguous weight-to-sequence-probability mappings and indeterminate parameter counts due to process tree equivalence. This paper abandons the conventional two-phase paradigm—first discovering a deterministic process tree, then assigning weights—and instead introduces, for the first time, a formal **Stochastic Process Tree (SPT)** framework. The SPT embeds probabilistic semantics directly into the process tree syntax, ensuring unique model parameters and unambiguous probabilistic interpretation. By integrating process mining, stochastic process modeling, and probabilistic language theory, the framework enables verifiable sequence probability inference. It eliminates uncertainties arising from model equivalence and weight definition, thereby establishing a rigorous theoretical foundation for interpretable and verifiable stochastic business process modeling.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Ambiguous impact of transition weights in stochastic Petri nets
• Undefined parameters in stochastic language of process trees
• Proposing stochastic process trees for clear parameter definition

Innovation

• Directly adding stochasticity to process trees
• Introducing stochastic process trees formalism
• Clarifying parameters and their stochastic impact