=Paper=
{{Paper
|id=Vol-3139/paper05
|storemode=property
|title=Probabilistic and Non-deterministic Event Data in Process Mining: Embedding Uncertainty in Process Analysis Techniques
|pdfUrl=https://ceur-ws.org/Vol-3139/paper05.pdf
|volume=Vol-3139
|authors=Marco Pegoraro
|dblpUrl=https://dblp.org/rec/conf/caise/000122
}}
==Probabilistic and Non-deterministic Event Data in Process Mining: Embedding Uncertainty in Process Analysis Techniques==
https://ceur-ws.org/Vol-3139/paper05.pdf
Probabilistic and Non-deterministic Event Data in
Process Mining: Embedding Uncertainty in Process
Analysis Techniques
Marco Pegoraro1
1
RWTH Aachen University, Ahornstraße 55, 52074 Aachen, Germany
Abstract
Process mining is a subfield of process science that analyzes event data collected in databases called
event logs. Recently, novel types of event data have become of interest due to the wide industrial
application of process mining analyses. In this paper, we examine uncertain event data. Such data contain
meta-attributes describing the amount of imprecision tied with attributes recorded in an event log. We
provide examples of uncertain event data, present the state of the art in regard of uncertainty in process
mining, and illustrate open challenges related to this research direction.
Keywords
process mining, process sciences, event data, probabilistic data, non-deterministic data
1. Introduction
Process mining is a rapidly growing subfield of data science that aims to automatically analyze
event data through a collection of techniques, including the extraction of a process model from a
log of historical process executions, the assessment of the conformance and deviations between
observed and expected behavior, and the measurement of metrics and indicators over event
data and process models.
The endemic adoption of process mining in the last decades has increased the demand of
domain-specific process analysis techniques—for instance, techniques to analyze less traditional
types of event data. In this paper, we describe novel types of event data—collectively referred
as uncertain event data [1]. Such data contain meta-attributes describing and quantifying the
amount of imprecision tied with attributes recorded in an event log. The uncertainty tied to an
event attribute might contain indications on its possible values, or also a probability distribution
over such values.
The aim of this research direction is to formally illustrate and classify different types of
uncertain event data, and develop ad-hoc process mining techniques able to natively function
with uncertain event data.
Proceedings of the Doctoral Consortium Papers Presented at the 34th International Conference on Advanced Information
Systems Engineering (CAiSE 2022), June 06–10, 2022, Leuven, Belgium
Envelope-Open pegoraro@pads.rwth-aachen.de (M. Pegoraro)
GLOBE https://mpegoraro.net/ (M. Pegoraro)
Orcid 0000-0002-8997-7517 (M. Pegoraro)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
Table 1
The strongly uncertain trace of an example of healthcare process. The timestamps column shows only
the day of the month.
Case ID Event ID Timestamp Activity Indeterminacy
ID192 𝑒1 5 NightSweats ?
ID192 𝑒2 8 PrTP, SecTP
ID192 𝑒3 4–10 Splenomeg
The remainder of the paper is structured as follows. Section 2 shows examples of uncertain
event data. Section 3 discusses some possible sources of uncertainty in recorded event data.
Section 4 explores related concepts in process mining and neighboring disciplines. Then,
Section 5 lays out the research methodology and describes the state of the art. Section 6
describes some open challenges in the field of uncertainty in process mining. Finally, Section 7
concludes the paper.
2. Uncertainty in Event Data
In order to more clearly visualize the structure of the attributes in uncertain events, let us
consider the following process instance, which is a simplified version of actually occurring
anomalies, e.g., in the processes of the healthcare domain.
An elderly patient enrolls in a clinical trial for an experimental treatment against myelopro-
liferative neoplasms, a class of blood cancers. This enrollment includes a lab exam and a visit
with a specialist; then, the treatment can begin. The lab exam, performed on the 8th of July,
finds a low level of platelets in the blood of the patient, a condition known as thrombocytopenia
(TP). During the visit on the 10th of July, the patient reports an episode of night sweats on
the night of the 5th of July, prior to the lab exam. The medic notes this but also hypothesizes
that it might not be a symptom, since it can be caused either by the condition or by external
factors (such as very warm weather). The medic also reads the medical records of the patient
and sees that, shortly prior to the lab exam, the patient was undergoing a heparin treatment (a
blood-thinning medication) to prevent blood clots. The thrombocytopenia, detected by the lab
exam, can then be either primary (caused by the blood cancer) or secondary (caused by other
factors, such as a concomitant condition). Finally, the medic finds an enlargement of the spleen
in the patient (splenomegaly). It is unclear when this condition has developed: it might have
appeared at any moment prior to that point. These events are collected and recorded in the
trace shown in Table 1 within the hospital’s information system.
Such scenario, with no known probability, is known as strong uncertainty. In this trace, the
rightmost column refers to event indeterminacy: in this case, 𝑒1 has been recorded, but it might
not have occurred in reality, and is marked with a “?” symbol. Event 𝑒2 has more then one
possible activity labels, either PrTP or SecTP. Lastly, event 𝑒3 has an uncertain timestamp, and
might have happened at any point in time between the 4th and 10th of July.
Uncertain events may also have probability values associated with them, a scenario defined
as weak uncertainty (Table 2). In the example described above, suppose the medic estimates
that there is a high chance (90%) that the thrombocytopenia is primary (caused by the cancer).
Furthermore, if the splenomegaly is suspected to have developed three days prior to the visit,
Table 2
A trace where uncertain event attributes are labeled with probabilities (weak uncertainty).
Case ID Event ID Timestamp Activity Indeterminacy
ID348 𝑒4 5 NightSweats ? ∶ 25%
PrTP: 90%,
ID348 𝑒5 8
SecTP: 10%
ID348 𝑒6 𝒩 (7, 1) Splenomeg
which takes place on the 10th of July, the timestamp of event 𝑒3 may be described through a
Gaussian curve with 𝜇 = 7. Lastly, the probability that the event 𝑒1 has been recorded but did
not occur in reality may be known (for example, it may be 25%).
Uncertain data as described here can be represented, imported, analyzed and exported on all
tools supporting the XES standard [2].
3. Sources of Uncertainty
In this section, we will examine some possible sources of uncertain event data. This is not
intended to be an exhaustive list nor a proper taxonomy, but it is rather a collection of motivating
situations not uncommon in the analysis of event data. In fact, many are documented in
literature.
It is important to notice that some causes of uncertainty are epistemic, that is, caused by a loss
of information or knowledge in some stage of the data recording process; or aleatoric, where
the uncertainty is intrinsic to the process itself. This distinction, strongly underlined in other
fields such as statistics and machine learning, is very important in order to interpret the results
of process mining analyses—especially in regard of process improvements prompted by the
analysis.
Data Coarseness. Limitations in the precision available to record an event attribute can
generate uncertainty. In process mining, this is often the case with timestamps, the attribute
we normally rely on to determine a total ordering between events. In some event logs, however,
timestamps of different events in the same process trace coincide, because of the coarseness of
data recording (e.g., when only the day is recorded but not the time, causing all events happened
in the same day to have the same timestamp). This is a source of partially ordered event data, a
type of uncertain data, and is well documented in process mining research [3].
Accuracy of Textual Information. In many processes, activities and other event attributes
are recorded by humans. In such cases, often natural language describes the activity identifier,
which may be imprecise in describing what actually happened. For instance, in the uncertain
trace of Table 1, the activity label uncertainty of event 𝑒2 might have been caused by the
activity being recorded simply as “TP”. This is also a known anomaly in process mining; some
approaches to repair it exist, and are based on merging similar labels through NLP methods [4].
Accuracy of Data Detection/Repair Methods. In some cases, events are not recorded
as they happen, but are rather detected from an unstructured source. An example of this is
detecting events from video feeds using e.g. deep learning [5, 6]. Neural networks are able to
predict the occurrence of an event describing it as probability distribution over the possible
classes (here, activity labels). This generates probabilistic information about events which fits
with the framework described in this paper.
4. Related Research
Techniques to deal with anomalies and noise in data are present in all branches of data science,
from statistics, to machine learning, to process mining itself. Often, a strong focus is on either
filter anomalous data [7], and analyze the remaining dataset, or repair anomalous attributes, by
predicting or inferring heuristically their correct value.
The meta-information describing uncertainty opens a third possibility, which is the develop-
ment of analysis techniques able to operate on uncertain data as-is. In the context of standard
tabular data, this is the research domain of probabilistic databases [8]. Specifically, an approach
that lies at the intersection of probabilistic databases and event data analysis is frequent itemsets
mining, where the goal is to define frequently-appearing clusters of objects across sets of items
(which might be events). There exist approaches to solve this problem for probabilistic data,
such as the U-Apriori algorithm [9].
The concept of uncertainty as quantifiable imprecision of data is also of great relevance in the
field of machine learning [10], and very recent research is aimed to detect possible uncertainties
in data, quantify them, and classify them as epistemic or aleatoric.
The topic of uncertainty in process mining as defined in this paper is novel, and—to the best
of our knowledge—no techniques able to manage uncertainty were described in literature before
the start of the doctoral program described in this paper. In the next section, we will describe
the research principle that leads our research of uncertain data, and examples of problems
solved by process mining techniques applied to uncertain data.
5. Research Methodology
The premises set out in Sections 2 and 3, together with the analysis of the literature, brought us
to formulate—among others—the following research questions:
RQ1: How can we adapt conformance checking to be able to deal with uncertain event data?
RQ2: How can we adapt process discovery to be able to deal with uncertain event data?
RQ3: How can we embed the mathematical formulation of uncertain event data to obtain
uncertain logs from information systems?
RQ4: How can we manage the high complexity tied with all possible scenarios described by an
uncertain trace?
In the following Subsections 5.1 and 5.2 we will describe the methodology utilized to research
RQ1 and RQ2, respectively. RQ3 and RQ4 entail challenges that are still completely open, and
we comment on them in Section 6.
Uncertain event data can be considered noise. Filtering or repairing noisy data in a pre-
processing step is standard practice both in process mining and data science at large. In our
research, the leading principle is the opposite: retain all data, and exploit the quantification of
uncertainty to analyze it in a trustworthy way. We shift the resolution of uncertainty from the
data side to the algorithm side. Such practice avoids information loss and unlocks new insights.
𝑡2
NightSweats
𝑡1 𝑡4 𝑡5 𝑡6
PrTP Adm
𝑡3
Splenomeg
Figure 1: A normative model for the healthcare process case in the running example. The initial marking
is displayed; the gray “token slot” represents the final marking.
Let us see this principle in action on two of the primary process mining analyses: conformance
checking (RQ1) and process discovery (RQ2).
5.1. Conformance Checking
Conformance checking is one of the main tasks in process mining, and consists in measuring
the deviation between process execution data and a reference model. This is particularly useful
for organization, since it enables them to compare historical process data against a normative
model created by process experts and to identify anomalies in their operations.
Let us assume that we have access to a normative model for the disease of the patient in the
running example, shown in Figure 1.
This model essentially states that the disease is characterized by the occurrence of night
sweats and splenomegaly on the patient, which may happen concurrently, and then should be
followed by primary thrombocytopenia. We would like to measure the conformance between
the trace in Table 1 and this normative model. A very popular conformance checking technique
works via the computation of alignments. Through this technique, we are able to identify the
deviations in the execution of a process, in the form of behavior happening in the model but
not in the trace, and behavior happening in the trace but not in the model. These deviations are
identified and used to compute a conformance score between the trace and the process model.
The formulation of alignments in is not applicable to an uncertain trace. In fact, depending
on the instantiation of the uncertain attributes of events—like the timestamp of 𝑒3 in the trace—
the order of event may differ, and so may the conformance score. However, we can look at
the best- and worst-case scenarios: the instantiation of attributes of the trace that entails the
minimum and maximum number of deviations with respect to the reference model. In our
example, two possible outcomes for the sample trace are ⟨NightSweats, Splenomeg, PrTP, Adm⟩
and ⟨SecTP, Splenomeg, Adm⟩; both represent the sequence of event that might have happened
in reality, but their conformance score is very different. The alignment of the first trace against
the reference model can be seen in Table 3, while the alignment of the second trace can be seen
in Table 4. These two outcomes of the uncertain trace in Table 1 represent, respectively, the
minimum and maximum amount of deviation possible with respect to the reference model, and
define then a lower and upper bound for conformance score.
It is possible to find bounds for the conformance score of an uncertain trace and a reference
process model with an extension of the alignment technique [11]. In order to find such bounds,
it is necessary to build a Petri net able to simulate all possible behaviors in the uncertain trace,
Table 3
An optimal alignment for ⟨NightSweats, Splenomeg, PrTP, Adm⟩, one of the possible instantiations of the
trace in Table 1, against the model in Figure 1. This alignment has a deviation cost of 0, and corresponds
to the best-case scenario for conformance between the process model and the uncertain trace.
≫ NightSweats Splenomeg ≫ PrTP Adm
𝜏 NightSweats Splenomeg 𝜏 PrTP Adm
𝑡1 𝑡2 𝑡3 𝑡4 𝑡5 𝑡6
Table 4
An optimal alignment for ⟨SecTP, Splenomeg, Adm⟩, one of the possible instantiations of the trace in
Table 1, against the model in Figure 1. This alignment has a deviation cost of 3, caused by 2 moves on
model and 1 move on log, and corresponds to the worst-case scenario for conformance between the
process model and the uncertain trace.
≫ SecTP ≫ Splenomeg ≫ ≫ Adm
𝜏 ≫ NightSweats Splenomeg 𝜏 PrTP Adm
𝑡1 𝑡2 𝑡3 𝑡4 𝑡5 𝑡6
called the behavior net [12]. The behavior net of the trace in Table 1 is shown in Figure 2.
The alignments in Tables 3 and 4 show how we can get actionable insights from process mining
over uncertain data. In some applications it is reasonable and appropriate to remove uncertain
data from an event log via filtering, and then compute log-level aggregate information—such as
total number of deviations, or average deviations per trace—using the remaining certain data.
Even in processes where this is possible, doing so prevents the important process mining task of
case diagnostic. Conversely, uncertain alignments allow not only to have best- and worst-case
scenarios for a trace, but also to individuate the specific deviations affecting both scenarios.
For instance, the alignments of the running example can be implemented in a system that
warns the medics that the patient might have been affected by a secondary thrombocytopenia
not explained by the model of the disease. Since the model indicates that the disease should
develop primary thrombocytopenia as a symptom, this patient is at risk of both types of platelets
deficit simultaneously, which is a serious condition. The medics can then intervene to avoid this
complication, and perform more exams to ascertain the cause of the patient’s thrombocytopenia.
(𝑒1 , 𝑁 𝑖𝑔ℎ𝑡𝑆𝑤𝑒𝑎𝑡𝑠) (𝑒2 , 𝑃𝑟𝑇 𝑃)
NightSweats PrTP
(start, 𝑒1 ) (𝑒1 , 𝑒2 ) (𝑒2 , 𝑒4 )
(𝑒1 , 𝜏 ) (𝑒2 , 𝑆𝑒𝑐𝑇 𝑃) (𝑒4 , 𝐴𝑑𝑚) (𝑒4 , end)
NightSweats SecTP Adm
(start, 𝑒3 ) (𝑒3 , 𝑆𝑝𝑙𝑒𝑛𝑜𝑚𝑒𝑔) (𝑒3 , 𝑒4 )
Splenomeg
Figure 2: The behavior net [13] representing the behavior of the uncertain trace in Table 1. The initial
marking is displayed; the gray “token slot” represents the final marking. This artifact is necessary to
perform conformance checking between uncertain traces and a reference model.
[80, 100]
[80, 80]
b e h
[80, 100] [0, 20] [0, 20]
[80, 80]
[100, 100] [0, 20] [15, 15] [15, 15]
a c [0, 20] [80, 100] g i
[0, 20] [0, 5]
[0, 5]
[0, 5] [0, 20] [80, 100]
[0, 5]
d f j
[0, 5]
Figure 3: The Uncertain Directly-Follows Graph (UDFG) computed based on the uncertain event log
⟨𝑎, 𝑏, 𝑒, 𝑓 , 𝑔, ℎ⟩80 , ⟨𝑎, {𝑏, 𝑐}, [𝑒, 𝑓 ], 𝑔, 𝑖⟩15 , ⟨𝑎, {𝑏, 𝑐, 𝑑}, [𝑒, 𝑓 ], 𝑔, 𝑗⟩5 . The arcs are labeled with the minimum and
maximum number of directly-follows relationship observable between activities in the corresponding
trace. The construction of this object is necessary to perform automatic process discovery over uncertain
event data.
5.2. Process Discovery
Process discovery is another main objective in process mining, and involves automatically
creating a process model from event data. Many process discovery algorithms rely on the
concept of directly-follows relationships between activities to gather clues on how to structure
the process model. Uncertain Directly-Follows Graphs (UDFGs) enable the representation of
directly-follows relationships in an uncertain event log; they consist in directed graphs where
the activity labels appearing in the event log constitute the nodes, and the edges are decorated
with information on the minimum and maximum frequency observable for the directly-follows
relation between pair of activities.
Let us examine an example of UDFG. In order to build a significant example, we need
to introduce an entire uncertain event log; since the full table notation for uncertain traces
becomes cumbersome for entire logs, let us utilize a shorthand simplified notation. In a trace, we
represent an uncertain event with multiple possible activity labels by listing all the associated
labels between curly braces.
When two events have mutually overlapping timestamps, we write their activity labels
between square brackets, and we indicate indeterminate events by overlining them. For instance,
the trace ⟨𝑎, {𝑏, 𝑐}, [𝑑, 𝑒]⟩ is a trace containing 4 events, of which the first is an indeterminate
event with activity label 𝑎, the second is an uncertain event that can have either 𝑏 or 𝑐 as activity
label, and the last two events have an interval as timestamp (and the two ranges overlap). Let
us consider the following event log:
⟨𝑎, 𝑏, 𝑒, 𝑓 , 𝑔, ℎ⟩80 , ⟨𝑎, {𝑏, 𝑐}, [𝑒, 𝑓 ], 𝑔, 𝑖⟩15 , ⟨𝑎, {𝑏, 𝑐, 𝑑}, [𝑒, 𝑓 ], 𝑔, 𝑗⟩5 .
For each pair of activities, we can count the minimum and maximum occurrences of a
directly-follows relationship that can be observed in the log. The resulting UDFG is shown in
Figure 3.
This graph can be then utilized to discover process models of uncertain logs via process
discovery methods based on directly-follows relationships. In a previous work we illustrated
h b e h
a e g a g
b f
i c f i
(a) A process model that can only replay the relationships (b) A process model that can replay some—but not all—
appearing in the certain parts of the traces in the the relationships appearing in the uncertain parts of
uncertain log. Here, information from uncertainty the traces in the uncertain log. This process model
has been excluded completely. mediates between representing only certain observa-
tion and representing all the possible behavior in the
process.
h
b e i
a c g
d f j
k
(c) A process model that can replay all possible configura-
tions of certain and uncertain traces in the uncertain
log. This process model has the highest possible re-
play fitness, but is also very likely to contain some
noisy or otherwise unwanted behavior.
Figure 4: Three different process models for the uncertain event log ⟨𝑎, 𝑏, 𝑒, 𝑓 , 𝑔, ℎ⟩80 , ⟨𝑎, {𝑏, 𝑐}, [𝑒, 𝑓 ], 𝑔, 𝑖⟩15 ,
⟨𝑎, {𝑏, 𝑐, 𝑑}, [𝑒, 𝑓 ], 𝑔, 𝑗⟩5 obtained through inductive mining over an uncertain directly-follows graph. The
different filtering parameters for the UDFG yield models with distinct features.
this principle by applying it to the inductive miner, a popular discovery algorithm [14]; the edges
of the UDFG can be filtered using the information on the labels, in such a way that the final
model can represent all possible behavior in the uncertain log, or only a part. Figure 4 shows
some process models obtained through inductive mining of the UDFG, as well as a description
regarding how the model relates to the original uncertain log. Notice how all three models
in the figure are not obtainable by filtering out the traces with uncertainty from the log; this
would radically remove useful information from the event log.
The process mining techniques described here are available in a Python library built on the
PM4Py framework [15].
6. Open Challenges
The examples shown in the previous section show some viable solutions to typical process
mining problems in the uncertain case; however, many technical challenges remain open.
A prominent problem is in data sourcing (RQ3). At the present time, no information system
natively supports the quantification of uncertainty, thus examples of uncertain logs come
from pre-processing steps that label data as uncertain based on domain knowledge provided
by process experts. This needs to be automated; for instance, intervening directly on the
process of data recording. Uncertainty-aware information systems would not only enable the full
automation of techniques for process mining over uncertainty, but also more reliably support
general data mining techniques, which would gain an additional measure of reliability.
Retaining all information from uncertain traces has the problem that the possible behavior
are subject to a combinatorial explosion (RQ4). While techniques to fully describe all behavior
and related probabilities exists [16], this comes at the cost of high (sometimes exponential)
computational complexity. In existing techniques, this has been mitigated by representing
uncertain traces as graphs (e.g., the behavior net), and designing algorithms able to work on
graphs as inputs. However, this is ineffective for some applications, such as measuring classic
model/log metrics in process mining like fitness and precision. We might overcome this problem
by switching to approximated techniques, which allow to trade-off speed and accuracy in a
controlled manner.
7. Conclusion
The research field of process mining on uncertain event data, while at its infancy, has proven
useful in solving real-life problems that can appear on uncertain data and that require dedicated
techniques. Such techniques do not filter out or repair the uncertain attributes in event logs,
but rather use extended versions of known process mining algorithms to obtain an uncertainty-
aware solution—a solution that explains uncertainty as intrinsic part of the process.
In pursuing this line of research, we aim to create a comprehensive set of techniques that
allow to carry out the most typical process mining tasks on data with quantified uncertainty.
Our future work will be guided by the open challenges hereby described which, once solved,
will enable a rich array of analysis techniques on uncertain data.
Acknowledgments
I am very grateful to Prof. Wil van der Aalst, who advises my doctoral studies, and to Dr. Merih
Seran Uysal, who supervises me in researching this topic. I thank the Alexander von Humboldt
(AvH) Stiftung for supporting my research interactions.
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