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Unbiased learning to rank has been proposed to alleviate the biases in thesearch ranking, making it possible to train ranking models with userinteraction data. In real applications, search engines are designed to displayonly the most relevant k documents from the retrieved candidate set. The restcandidates are discarded. As a consequence, position bias and sample selectionbias usually occur simultaneously. Existing unbiased learning to rankapproaches either focus on one type of bias (e.g., position bias) or mitigatethe position bias and sample selection bias with separate components,overlooking their associations. In this study, we first analyze the mechanismsand associations of position bias and sample selection bias from the viewpointof a causal graph. Based on the analysis, we propose Causal LikelihoodDecomposition (CLD), a unified approach to simultaneously mitigating these twobiases in top-k learning to rank. By decomposing the log-likelihood of thebiased data as an unbiased term that only related to relevance, plus otherterms related to biases, CLD successfully detaches the relevance from positionbias and sample selection bias. An unbiased ranking model can be obtained fromthe unbiased term, via maximizing the whole likelihood. An extension to thepairwise neural ranking is also developed. Advantages of CLD includetheoretical soundness and a unified framework for pointwise and pairwiseunbiased top-k learning to rank. Extensive experimental results verified thatCLD, including its pairwise neural extension, outperformed the baselines bymitigating both the position bias and the sample selection bias. Empiricalstudies also showed that CLD is robust to the variation of bias severity andthe click noise.

Unbiased Top-k Learning to Rank with Causal Likelihood Decomposition