An offline metric for the debiasedness of click models

A well-known problem when learning from user clicks are inherent biases prevalent in the data, such as position or trust bias. Click models are a common method for extracting information from user clicks, such as document relevance in web search, or to estimate click biases for downstream applications such as counterfactual learning-to-rank, ad placement, or fair ranking. Recent work shows that the current evaluation practices in the community fail to guarantee that a well-performing click model generalizes well to downstream tasks in which the ranking distribution differs from the training distribution, i.e., under covariate shift. In this work, we propose an evaluation metric based on conditional independence testing to detect a lack of robustness to covariate shift in click models. We introduce the concept of debiasedness and a metric for measuring it. We prove that debiasedness is a necessary condition for recovering unbiased and consistent relevance scores and for the invariance of click prediction under covariate shift. In extensive semi-synthetic experiments, we show that our proposed metric helps to predict the downstream performance of click models under covariate shift and is useful in an off-policy model selection setting