  Click data collected by modern recommendation systems are an important source
of observational data that can be utilized to train learning-to-rank (LTR)
systems. However, these data suffer from a number of biases that can result in
poor performance for LTR systems. Recent methods for bias correction in such
systems mostly focus on position bias, the fact that higher ranked results
(e.g., top search engine results) are more likely to be clicked even if they
are not the most relevant results given a user's query. Less attention has been
paid to correcting for selection bias, which occurs because clicked documents
are reflective of what documents have been shown to the user in the first
place. Here, we propose new counterfactual approaches which adapt Heckman's
two-stage method and accounts for selection and position bias in LTR systems.
Our empirical evaluation shows that our proposed methods are much more robust
to noise and have better accuracy compared to existing unbiased LTR algorithms,
especially when there is moderate to no position bias.
