  The Unbiased Learning-to-Rank framework has been recently proposed as a
general approach to systematically remove biases, such as position bias, from
learning-to-rank models. The method takes two steps - estimating click
propensities and using them to train unbiased models. Most common methods
proposed in the literature for estimating propensities involve some degree of
intervention in the live search engine. An alternative approach proposed
recently uses an Expectation Maximization (EM) algorithm to estimate
propensities by using ranking features for estimating relevances. In this work
we propose a novel method to directly estimate propensities which does not use
any intervention in live search or rely on modeling relevance. Rather, we take
advantage of the fact that the same query-document pair may naturally change
ranks over time. This typically occurs for eCommerce search because of change
of popularity of items over time, existence of time dependent ranking features,
or addition or removal of items to the index (an item getting sold or a new
item being listed). However, our method is general and can be applied to any
search engine for which the rank of the same document may naturally change over
time for the same query. We derive a simple likelihood function that depends on
propensities only, and by maximizing the likelihood we are able to get
estimates of the propensities. We apply this method to eBay search data to
estimate click propensities for web and mobile search and compare these with
estimates using the EM method. We also use simulated data to show that the
method gives reliable estimates of the "true" simulated propensities. Finally,
we train an unbiased learning-to-rank model for eBay search using the estimated
propensities and show that it outperforms both baselines - one without position
bias correction and one with position bias correction using the EM method.
