# Scalar is Not Enough: Vectorization-based Unbiased Learning to Rank

arXiv: https://arxiv.org/abs/2206.01702 · HTML: https://mlsanity.com/paper/2206.01702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 14 of 14)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [Fast Matrix Factorization for Online Recommendation with Implicit Feedback](https://mlsanity.com/paper/1708.05024/) (2017)
- [Unbiased Learning to Rank with Unbiased Propensity Estimation](https://mlsanity.com/paper/1804.05938/) (2018)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Correcting for Selection Bias in Learning-to-rank Systems](https://mlsanity.com/paper/2001.11358/) (2020)
- [Estimating Position Bias without Intrusive Interventions](https://mlsanity.com/paper/1812.05161/) (2018)
- [Cascade Model-based Propensity Estimation for Counterfactual Learning to Rank](https://mlsanity.com/paper/2005.11938/) (2020)
- [Intervention Harvesting for Context-Dependent Examination-Bias Estimation](https://mlsanity.com/paper/1811.01802/) (2018)
- [A Click Sequence Model for Web Search](https://mlsanity.com/paper/1805.03411/) (2018)
- [Unbiased Learning to Rank: Online or Offline?](https://mlsanity.com/paper/2004.13574/) (2020)
- [A Deep Recurrent Survival Model for Unbiased Ranking](https://mlsanity.com/paper/2004.14714/) (2020)
- [Counterfactual Learning to Rank using Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2007.09798/) (2020)
- [Eliminating Search Intent Bias in Learning to Rank](https://mlsanity.com/paper/2002.03203/) (2020)

## Built on by (most cited first, 2 of 2)

- [Towards Disentangling Relevance and Bias in Unbiased Learning to Rank](https://mlsanity.com/paper/2212.13937/) (2022)
- [Identifiability Matters: Revealing the Hidden Recoverable Condition in Unbiased Learning to Rank](https://mlsanity.com/paper/2309.15560/) (2023)

## Abstract (arXiv)

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.