{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/scalar-is-not-enough-vectorization-based","title":"Scalar is Not Enough: Vectorization-based Unbiased Learning to Rank","arxiv_id":"2206.01702","date":"2022-06-03","proceeding":null,"authors":["Mouxiang Chen","Chenghao Liu","Zemin Liu","Jianling Sun"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2206.01702v2","url_pdf":"https://arxiv.org/pdf/2206.01702v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"scalar-is-not-enough-vectorization-based","repo_url":"https://github.com/keytoyze/vectorization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"learning-to-rank","task_name":"Learning-To-Rank"}],"methods":[{"method_slug":"base","method_name":"BASE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.01702","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.01702"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/keytoyze/vectorization","reach":null}],"summary":{"ran_fixture":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"a354ed46ddacc027","entry":"py_aggregate","repo":"keytoyze/vectorization","repo_kind":"official","path":"ultra/learning_algorithm/vectorization.py","file_url":"https://github.com/keytoyze/vectorization/blob/HEAD/ultra/learning_algorithm/vectorization.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"a354ed46ddacc027"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}