# Explainability of Predictive Process Monitoring Results: Can You See My Data Issues?
## 2 Background
### Predictive Process Monitoring  
A process instance is the execution of certain activities allowed in the context of a given business process. Predictive Process Monitoring (PPM) is a process mining use case that supports decision makers with predictions of the future course of a running process instance. This goal is realised by building models to generate predictions such as the next activity to be carried out, time-related information (e.g., the remaining time until process completion), the outcome of the process instance, execution costs, and executing resource [1]. The generation of a specific prediction is referred to as a _PPM task_. A PPM task takes an event log as its central input; the event log documents the execution history of the instances of a business process in terms of _traces_. In turn, each trace represents the execution events of a single process instance. For example, in an event log documenting a loan application process, each case, i.e., a process instance, represents a specific application process. Table 1 provides an example of a loan application process event log. Each case is composed of mandatory components and optional ones. Note that we use the terms case and process instance interchangeably here to refer to the same concept; however, we tend to use the term _case_ where the data view of a business process is our concern and the term _process instance_ when we are concerned with the conceptual view of a business process. Trace, Event Log.Let \(\varepsilon\) be the set of all possible events that may take place during the execution of a business process, i.e., the event universe. A trace \(\sigma=<e_{1},e_{2},e_{3},\ldots,e_{n}>\), with \(n\in\mathbb{N}\) being the total number of events that occurred during the execution of a process instance. A trace contains at least one event. Let D be the universe of data attributes associated with each event; then, \(d_{ij}\in\mathbb{D}\), where \(i\) is the event number and \(j\in\mathbb{M}\) is the number of data attributes associated with the event. A case corresponds to \(<(e_{1},(d_{11},d_{12},\ldots,d_{1m})),(e_{2},(d_{21},d_{22},\ldots,d_{2m})),( e_{3},(d_{31},d_{32},\ldots,d_{3m})),\ldots,(e_{n},(d_{n1},d_{n2},\ldots,d_{nm}))>\). An event with its associated attributes must not take place more than once in a case, i.e., no redundancy is allowed when storing events associated with the same case. An event log (L) corresponds to a set of cases, in which each event appears at most once in the entire event log [1]. As mandatory attributes, a case should contain [1]:  
* Case ID: represents a unique identifier of the case in the whole event log. \begin{table}
\begin{tabular}{|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|} \hline \multicolumn{1}{c|}{\multirow{2}{*}{**Case ID ID**}} & \multicolumn{4}{c|}{**Dynamic Attributes**} \\ \cline{2-9}  & \multicolumn{1}{c|}{**Static Attributes**} & & & & \\ \hline \multicolumn{1}{c|}{\multirow{2}{*}{**Case ID ID**}} & \multicolumn{1}{c|}{**Activity**} & \multicolumn{1}{c|}{**Applicant ID ID**} & \multicolumn{1}{c|}{**Timestamp ID**} & \multicolumn{1}{c|}{**Resource**} & \multicolumn{1}{c|}{**Requested ID**} & \multicolumn{1}{c|}{**Granted ID**} & \multicolumn{1}{c|}{**Monthly Conf.**} \\ \hline \hline A150 & Create Application & C1820 & 30 March 2018 & [PERSON] & 38,000 & 30,000 & 1281 \\ \hline A150 & Validate Application & C1820 & 30 March 2018 & [PERSON] & 38,000 & 30,000 & 231 \\ \hline A150 & Decide & C1820 & 12 April 2018 & [PERSON] & 38,000 & 30,000 & 342 \\ \hline A150 & Close Application & C1820 & 23 April 2018 & [PERSON] & 38,000 & 30,000 & 1213 \\ \hline A218 & Create Application & C9121 & 15 March 2018 & [PERSON] & 57,000 & 44,000 & 643 \\ \hline A218 & Validate Application & C9121 & 5 April 2018 & [PERSON] & 57,000 & 44,000 & 342 \\ \hline A562 & Close Application & C7238 & 30 Dec 2018 & [PERSON] & 20,000 & 17,000 & 500 \\ \hline \end{tabular}
\end{table} 
Table 1: Example loan application event log.