  Unbiased learning to rank (ULTR) aims to train an unbiased ranking model from
biased user click logs. Most of the current ULTR methods are based on the
examination hypothesis (EH), which assumes that the click probability can be
factorized into two scalar functions, one related to ranking features and the
other related to bias factors. Unfortunately, the interactions among features,
bias factors and clicks are complicated in practice, and usually cannot be
factorized in this independent way. Fitting click data with EH could lead to
model misspecification and bring the approximation error.
  In this paper, we propose a vector-based EH and formulate the click
probability as a dot product of two vector functions. This solution is complete
due to its universality in fitting arbitrary click functions. Based on it, we
propose a novel model named Vectorization to adaptively learn the relevance
embeddings and sort documents by projecting embeddings onto a base vector.
Extensive experiments show that our method significantly outperforms the
state-of-the-art ULTR methods on complex real clicks as well as simple
simulated clicks.
