Statistical process discovery

TL;DR

We present a simulation-based framework for stochastic process discovery that replaces costly exact computation of the stochastic language with arbitrarily precise approximations obtained by synchronizing a stochastic model with a language detector automaton. The method uses an $ABC$-SMC scheme over transition weights to minimize the $rEMD$ between the model language $L_{N_s}$ and the log language $L_E$, enabled by HASL-based language estimation. Experiments on real-life event logs show ABC-SMC–HASL often yields lower $rEMD$ than unfolding-based optimization, weight estimators, or SLPN approaches, while maintaining competitive runtimes and providing posterior insights into weight importance. The work demonstrates scalable conformance checking for stochastic process discovery and offers a practical, parallelizable route to learning probabilistic process models from data.

Abstract

Stochastic process discovery is concerned with deriving a model capable of reproducing the stochastic character of observed executions of a given process, stored in a log. This leads to an optimisation problem in which the model's parameter space is searched for, driven by the resemblance between the log's and the model's stochastic languages. The bottleneck of such optimisation problem lay in the determination of the model's stochastic language which existing approaches deal with through, hardly scalable, exact computation approaches. In this paper we introduce a novel framework in which we combine a simulation-based Bayesian parameter inference scheme, used to search for the ``optimal'' instance of a stochastic model, with an expressive statistical model checking engine, used (during inference) to approximate the language of the considered model's instance. Because of its simulation-based nature, the payoff is that, the runtime for discovering of the optimal instance of a model can be easily traded in for accuracy, hence allowing to treat large models which would result in a prohibitive runtime with non-simulation based alternatives. We validate our approach on several popular event logs concerning real-life systems.