## 2 Background
### Limitations of Association Rule Mining and Regression Analysis  
Uncovering biases from observational data requires a thorough exploratory analysis of the data, as well as rigorous estimations of effect sizes. Whereas the literature generally considers association rule mining for the former, regression models are often used to evaluate effect sizes and rigorously evaluate evidence in the data. However, both methods have intrinsic shortcomings in our application. We then discuss these shortcomings, which are summarized in Table 3.  
**Association Rule Mining.** First, rule mining requires an analyst to carefully tune the threshold parameters for the used relevance metrics without providing a rigorous way to 'prioritize' rules for a certain outcome. While selecting low threshold values can lead to  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Data-** & **No Param.** & **Feature** & **Feature** & **Change** \\  & **Agnostic** & **Tuning** & **Level** & **Value Level** & **Impact** \\ \hline Assoc. Rule Mining & \(\bullet\) & \(\bigcirc\) & \(\bigcirc\) & \(\bullet\) & \(\bigcirc\) \\ Regression Analysis & \(\bigcirc\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of association rule mining and regression analysis with respect to the identified desiderata for bias detection in Table 2, where \(\bullet\) means “support” and \(\bigcirc\) “no support”.  
a large number of rules, most of which are not interesting and/or not reliable, excessively high values can easily lead to missing relevant correlations. Rule mining also lacks support for the statistical validation of the associations detected among the variables. The use of metrics such as support and confidence does not guarantee preventing the generation of _false discoveries_, such as rules showing dependencies likely due by chance, or rules where the antecedent contains items that are actually independent of the consequent [13]. Moreover, association rule mining only allows analysts to explore relations among single feature values and class values (feature value level analysis), while feature level analysis is not supported.  
**Regression analysis.** Compared to association rule mining, regression analysis provides a more robust approach to statistical validation. The output provided by regression techniques supports both feature level and feature value level analysis. Moreover, they do not require the tuning of parameters. However, regression (parametric) approaches require some type of hypothesis formulation to build a model to regress on. This is desirable in general as it attaches semantic meaning to the statistical evidence found in the data. However, for data exploration tasks such as the one at hand, regression approaches are very limited in nature. _Forward_ or _backward_ model selection procedures [7] can be applied to identify the 'best' model explaining the data, but the number of models to be compared explodes exponentially as the number of allowed variable interactions increases. More importantly, there is no 'guarantee' that the resulting selected 'best' model has any useful interpretation that can be used to take action and tackle the decision bias at the source.