-For details about the bias estimation, users are encouraged to visit the original paper. We will briefly go through the intuition behind the algorithm in this section. When conducting a study, we might accidentally introduce selection bias to the experiment by selecting subjects with certain conditions not being distributed evenly. For instance, in a medical study, the group of patients selected to be part of the treatment group might consist of only a particular range of age. If this happens, then we have introduced age as a confounding variable in the study. The effect (or the lack thereof) might be caused by age instead of by the effect of the treatment. However, if we know the confounder (the age), we can use the (extended) inverse propensity score to re-weight the data and remove the bias introduced in the study. The propensity score is defined as the probability of a patient receiving the treatment given all the relevant conditions. In the context of learning to rank, the position bias is cast as a form of selection bias, a user might not observe a document if it's placed at the end of the list. As a result, that document is not selected to be judged by the user and cannot be clicked.
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