  Accurate estimates of examination bias are crucial for unbiased
learning-to-rank from implicit feedback in search engines and recommender
systems, since they enable the use of Inverse Propensity Score (IPS) weighting
techniques to address selection biases and missing data. Unfortunately,
existing examination-bias estimators are limited to the Position-Based Model
(PBM), where the examination bias may only depend on the rank of the document.
To overcome this limitation, we propose a Contextual Position-Based Model
(CPBM) where the examination bias may also depend on a context vector
describing the query and the user. Furthermore, we propose an effective
estimator for the CPBM based on intervention harvesting. A key feature of the
estimator is that it does not require disruptive interventions but merely
exploits natural variation resulting from the use of multiple historic ranking
functions. Real-world experiments on the ArXiv search engine and semi-synthetic
experiments on the Yahoo Learning-To-Rank dataset demonstrate the superior
effectiveness and robustness of the new approach.
