Process mining techniques are useful for analyzing and optimizing processes. However, processes often exist in many variants that can differ significantly in their execution. These differences within the data can negatively affect the quality of process mining results and, furthermore, indicate disparities within the process. While several approaches exist that characterize the differences between processes, oftentimes the mere existence of differences can be problematic. To this end, techniques to prove or disprove the existence of such differences are required and should do so in a statistically sound manner. However, the literature on process hypothesis testing is sparse and limited in the considered dimensions of difference. In this paper, we propose a hypothesis testing approach that uses the earth mover’s distance in combination with a permutation test to compare event logs in various dimensions. The evaluation shows that the proposed approach achieves better performance than the existing work in detecting control-flow differences and, moreover, detects differences in further dimensions, demonstrated on the time dimension.

Abstract Process mining aids organisations in improving their operational processes by providing visualisations and algorithms that turn event data into insights. How often behaviour occurs in a process—the stochastic perspective—is important for simulation, recommendation, enhancement and other types of analysis. Although the stochastic perspective is important, the focus is often on control flow. Stochastic conformance checking techniques assess the quality of stochastic process models and/or event logs with one another. In this paper, we address three limitations of existing stochastic conformance checking techniques: inability to handle uncertain event data (e.g. events having only a date), exponential blow-up in computation time due to the analysis of all interleavings of concurrent behaviour and the problem that loops that can be unfolded infinitely often. To address these challenges, we provide bounds for conformance measures and use partial orders to encode behaviour. An open-source implementation is provided, which we use to illustrate and evaluate the practical feasibility of the approach.

Traditional process models like Petri nets effectively describe the control flow of processes but fail to capture stochastic information such as choice likelihoods. To address this, Stochastic Labeled Petri Nets (SPNs) have recently gained attention, extending Petri nets with transition weights that allow to associate executions with probabilities. The language of an SPN thereby becomes a probability distribution over traces (i.e., sequences of activities). To assess an SPN’s quality, Earth Mover’s Stochastic Conformance (EMSC) emerged as a natural metric that measures the similarity of the SPN’s trace distribution to the observed real-world distribution. In this paper, we propose a locally optimal approach for fine-tuning (or finding) transitions weights to maximize an SPN’s EMSC. Leveraging the relationship between EMSC and the Wasserstein distance, which recently gained attention as a loss function in machine learning, we compute subgradients for EMSC to optimize transition weights via subgradient descent. Besides, we propose a straightforward solution to handle models that allow for infinitely many traces. Our optimization approach is broadly applicable for EMSC—that is, for EMSC using arbitrary trace-to-trace distances—unlike existing works that either to not explicitly consider EMSC or only special variants. We demonstrate the applicability of our approach on several real-life event logs and discovery algorithms, comparing it to state-of-the-art stochastic process discovery methods and a recent full automated simulation approach.

Process mining provides techniques to learn models from event data. These models can be descriptive (e.g., Petri nets) or predictive (e.g., neural networks). The learned models offer operational support to process owners by conformance checking, process enhancement, or predictive monitoring. However, processes are frequently subject to significant changes, making the learned models outdated and less valuable over time. To tackle this problem, Process Concept Drift (PCD) detection techniques are employed. By identifying when the process changes occur, one can replace learned models by relearning, updating, or discounting pre-drift knowledge. Various techniques to detect PCDs have been proposed. However, each technique's evaluation focuses on different evaluation goals out of accuracy, latency, versatility, scalability, parameter sensitivity, and robustness. Furthermore, the employed evaluation techniques and data sets differ. Since many techniques are not evaluated against more than one other technique, this lack of comparability raises one question: How do PCD detection techniques compare against each other? With this paper, we propose, implement, and apply a unified evaluation framework for PCD detection. We do this by collecting evaluation goals and evaluation techniques together with data sets. We derive a representative sample of techniques from a taxonomy for PCD detection. The implemented techniques and proposed evaluation framework are provided in a publicly available repository. We present the results of our experimental evaluation and observe that none of the implemented techniques works well across all evaluation goals. However, the results indicate future improvement points of algorithms and guide practitioners.

Modern business processes are embedded in a complex environment and, thus, subjected to continuous changes. While current approaches focus on the control flow only, additional perspectives, such as time, are neglected. In this paper, we investigate a more general concept drift detection framework that is based on the Earth Mover's Distance. Our approach is flexible in terms of incorporating additional perspectives thanks to the capability of defining custom feature representations, as well as expressive feature similarity measures. We demonstrate the former by incorporating the time perspective using both a time-binning-based trace descriptor and a suitable similarity measure that considers time and control flow. We evaluate the resulting sliding window detector on different types of control-flow and time drifts, and holistic drifts involving multiple perspectives.