The application of Unbiased Learning to Rank (ULTR) is widespread in modern systems for training unbiased ranking models from biased click logs. The key is to explicitly model a generation process for user behavior and fit click data based on examination hypothesis. Previous research found empirically that the true latent relevance can be recovered in most cases as long as the clicks are perfectly fitted. However, we demonstrate that this is not always achievable, resulting in a significant reduction in ranking performance. In this work, we aim to answer if or when the true relevance can be recovered from click data, which is a foundation issue for ULTR field. We first define a ranking model as identifiable if it can recover the true relevance up to a scaling transformation, which is enough for pairwise ranking objective. Then we explore an equivalent condition for identifiability that can be novely expressed as a graph connectivity test problem: if and only if a graph (namely identifiability graph, or IG) constructed on the underlying structure of the dataset is connected, we can guarantee that the relevance can be correctly recovered. When the IG is not connected, there may be bad cases leading to poor ranking performance. To address this issue, we propose two methods, namely node intervention and node merging, to modify the dataset and restore connectivity of the IG. Empirical results obtained on a simulation dataset and two LTR benchmark datasets confirm the validity of our proposed theorems and show the effectiveness of our methods in mitigating data bias when the relevance model is unidentifiable.

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