Process mining aims to obtain insights from event logs. In this extended abstract, we will show that it is useful to take the frequency perspective (that is, stochastic behaviour) into account, and will discuss several stochastic process mining techniques. Organisations run on processes: processing an order, onboarding a new hire, getting travel approval; many work performed in organisations can be considered as processes. Process mining aims to optimise these processes through event logs: records of executions of processes, typically obtained from information systems that support the processes. Figure 1 shows an overview the context and common tasks of process mining. A process is running in an organisation, and through information systems an event log is recorded. Using a process discovery technique, a process model can be discovered. Process discovery techniques need to trade-of several potentially competing model quality aspects, such as readability and filtering noise. Ideally, a process model would be compared to the actual process, however as that is assumed to be unknown, this relation can only be theoretically proven under certain assumptions, or estimated. Rather, in practice a model should be compared to (a separate test) event log, for instance on the quality dimensions of simplicity, fitness - the fraction of behaviour in the event log that is in the process model, and precision - the fraction of behaviour of the model that was observed in the event log. A process model expresses a set of potential traces that the model supports, and it may be dificult to fully interpret insights gained from such a model by itself. Therefore, in process mining projects, the model is typically enhanced with frequency or performance information, after which the project may continue with repeated drill-down filters, hypotheses and verification [ 1]. In more advanced settings, process models can be
? process prove/estimate conformance
event log execute
enhance discover check conformance process model simulation
analysis
recommendation
simulated. This provides a baseline for, after applying certain changes, comparing
process redesigns in a what-if analysis. Finally, if process mining is integrated into daily
operations, process models can be used to recommend interventions for traces that are
still in the process [
Let us consider two event logs:
L1 = [⟨register, check, accept⟩10000,
L2 = [⟨register, check, accept⟩9500, ⟨register, check, reject⟩10000, ⟨register, accept⟩1] ⟨register, check, reject⟩9500 ⟨register, accept⟩1001] These logs have an equivalent control flow: the set of traces in both logs is the same. However, it is obvious that these logs are not from the same process: in L1, ⟨register, accept⟩ occurs once, while in L2 it occurs more than a thousand times. Any process mining techniques ignoring the stochastic perspective will consider these logs as to come from the Thus, these logs are diferent mostly because of their frequencies; in process models, we refer to this as the stochastic perspective.
The stochastic perspective is obviously present in a process: behaviour has a certain likelihood of appearing. Consequently, an event log derived from a process also has a stochastic perspective: behaviour has a certain likelihood of being recorded in the event log. Thus, the stochastic perspective is there.
On th right side of Figure 1, we need an idea of how often behaviour occurs in order to
perform analysis: it matters whether behaviour is exceptional or common, and average
performance measures are weighted by definition on the multiplicity of behaviour. For
simulation, simulation software needs to know how likely each path or decision in the
process is. Similarly, recommendation needs to be aware of how likely behaviour is in
order to steer towards more likely favourable outcomes [
Without existing stochastic process models, existing analysis, simulation and
recommendation techniques, which inherently use the stochastic perspective, must obtain this
stochastic information in an ad-hoc fashion from the event log [
Another area where considering stochastic process information is beneficial is in the evaluation of process models: we already discussed fitness, and most fitness measures take the stochastic information into account implicitly: the more likely behaviour in the log, the higher its influence on the fitness measure. Precision measures express the fraction of behaviour of the model that was seen in the event log: precision = |model ∩ log| |model| An inherent problem with this intuitive informal definition is that one needs a count of behaviour in the model. One cannot simply count traces, as models may express infinitely much behaviour through loops.
We illustrate this for one non-stochastic precision technique [
For a stochastic process model, this is not a problem as we have a notion of size: in the state space, it is known exactly how likely each edge is, and that is exactly equal to the size – the probability mass – of the model that lies behind it. Thus, for stochastic process models more intuitive precision measures can be defined.
If we consider Figure 1 again, inaccuracies or imprecisions can be introduced at many
steps of these common process mining tasks:
• When recording the event log from a process, the quality of the recording may vary,
or extraction may be biased;
• When discovering a process model, a process discovery technique may need to make
well-known trade-ofs between potentially competing quality criteria;
• When estimating the quality of a process model with respect to the process,
assumptions and bias may be tested based on a process model [
All of these steps may be sources of inaccuracies and imprecisions, which may propagate
and aggregate over a process mining project. We conjecture that the use of stochastic
process models makes it easier to quantify and study these inaccuracies and imprecisions,
such that the reliability of conclusions can be quantified [
Next, we discuss some stochastic process mining techniques that mimic standard nonstochastic techniques: stochastic process discovery and stochastic conformance checking. Furthermore, we discuss completely new types of techniques that require considering stochastic process behaviour.
In stochastic process discovery, the aim is to automatically discover a stochastic process
model – such as a stochastic labelled Petri net [
A technique that does not start from an existing is [
A completely diferent approach is taken by [
A stochastic conformance checking technique compares with one another an event log
and a stochastic process model, or two stochastic process models, or two event logs.
Stochastic entropy [
Another stochastic conformance checking technique is the Earth Movers’ Distance [
Next to stochastic extensions of techniques, the concept of stochastic process behaviour has enabled some new types of analyses and techniques.
Some event logs have hundreds of activities, which make them challenging to analyse.
A way to simplify models is to apply a trace-based filter, thereby focusing the analysis on,
for instance, platinum customers, or orders with a value over a certain amount. Cohort
analysis recommends filters based on the diference between traces that pass the filter and
all the other traces: the filter that is associated with the largest diference in stochastic
behaviour would simplify the model the most [
Most process mining insights are associational. However, as in associational insights
there is no diference between cause and efect, for redesign or what-if analyses it is
beneficial to perform causal reasoning. Recent studies have introduced causal reasoning:
to discover causal rules from event logs [
Further techniques targeting stochastic behaviour are the detection of diferences in
a stochastic process over time (concept drift) [
Process mining is an exciting field of research. In this pledge for consideration of the stochastic perspective of process behaviour, we have shown several challenges of process mining concepts and techniques that may benefit from having a stochastic perspective. Several recent stochastic process mining techniques were discussed, both dropin replacements for well-known process discovery and conformance checking techniques, as well as new techniques that leverage the stochastic perspective of behaviour of event logs to enable new types of analysis.