# Position Bias Estimation for Unbiased Learning-to-Rank in eCommerce Search

## TL;DR

This paper introduces a novel, non-interventional method to estimate position bias in eCommerce search by leveraging natural rank changes over time, improving unbiased learning-to-rank models.

## Contribution

The authors propose a direct propensity estimation technique based on natural rank variations, avoiding live intervention or relevance modeling, and demonstrate its effectiveness on eBay data.

## Key findings

- The new method produces reliable propensity estimates on real and simulated data.
- Unbiased learning-to-rank models trained with these estimates outperform baselines.
- The approach is applicable to any search engine with natural rank fluctuations.

## Abstract

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.