## 2 Background  
We model a decision-making process as a set of records comprising a number of attributes (hereafter called _variables_ or _features_) describing a given subject (e.g., a person applying for a loan) and the _outcome_ of the process, i.e., the decision made for the subject. Intuitively, each record represents one observation of the process along with the data upon which it operated (i.e., the variables) and its outcome. Table 1 provides a fictional example of a decision-making process of a financial institute aiming to determine whether a given applicant should be classified as a high-risk individual, i.e., they are likely unable to refund a loan. Each record corresponds to a single loan request where SubjID provides the ID of the applicant and Employed, Income, Gender, Ethnic Group are variables characterizing the applicant. HighRisk is the binary variable describing the outcome of the process (1 encoding a 'high-risk' evaluation for that subject). Decisional processes are often affected by human or algorithmic bias. In the example above, the data could reveal to an observer whether being currently employed is a relevant criterion for the bank's decision-making process. Similarly, it could reveal how the odds of being assigned to a risk category change for every additional dollar of income. Whereas these are relations that one could reasonably expect to find in any decision process of this type, other complex dynamics can have a 'hidden' impact on the decision. For example, Ethnic Group may have an impact, albeit perhaps more so below certain Income levels. A recent example of such potentially systematic biases can be found in the Netherlands; in January 2021, the national Dutch government resigned following a scandal involving unfair accusations against Dutch residents related to child benefit support. These accusations turned out to disproportionately target residents with dual nationalities and of specific ethnic origins requesting financial support for childcare from the Dutch government ([[https://www.theguardian.com/world/2021/jan/15/dutch-government-resigns-over-child-benefits-scandal](https://www.theguardian.com/world/2021/jan/15/dutch-government-resigns-over-child-benefits-scandal)]([https://www.theguardian.com/world/2021/jan/15/dutch-government-resigns-over-child-benefits-scandal](https://www.theguardian.com/world/2021/jan/15/dutch-government-resigns-over-child-benefits-scandal)), Last accessed 16 March 2022). Similarly, Gender or belief-related biases can interact with other variables, such as Ethnic Group or social status, to affect a decision. To detect biases in decisional processes, one has to quantify to what extent the use of variables (e.g., Gender, Ethnic Group) has influenced the process outcome. A main challenge lies in the fact that the decisional process is often unknown. We only observe the output of a black-box process. Therefore, detecting biases in decisional processes requires reconstructing the decisional process from observational data and determining which variables were most likely used for decision making. Operationally, the problem can be formulated as deriving possible _correlations_ between variables and the process outcome (i.e., to indicate the fact that individuals with certain attributes have higher chances of obtaining a certain outcome than individuals without those attributes). We argue that any approach designed to tackle this challenge should meet a number of desiderata, as reported in Table 2.  
The last three desiderata concern the capability of the approach to enable the understanding of how features and their values impact the outcome of the decisional process. Two classes of techniques are widely used for the exploration of observational data: _(i)_ approaches that use statistical tools, in particular _regression analysis_, to determine which variables are more likely able to explain the process outcome and _(ii)_ approaches based