{"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/linear-predictor-on-linearly-generated-data","title":"Linear predictor on linearly-generated data with missing values: non consistency and solutions","arxiv_id":"2002.00658","date":"2020-02-03","proceeding":null,"authors":["Marine Le Morvan","Nicolas Prost","Julie Josse","Erwan Scornet","Gaël Varoquaux"],"abstract":"We consider building predictors when the data have missing values. We study the seemingly-simple case where the target to predict is a linear function of the fully-observed data and we show that, in the presence of missing values, the optimal predictor may not be linear. In the particular Gaussian case, it can be written as a linear function of multiway interactions between the observed data and the various missing-value indicators. Due to its intrinsic complexity, we study a simple approximation and prove generalization bounds with finite samples, highlighting regimes for which each method performs best. We then show that multilayer perceptrons with ReLU activation functions can be consistent, and can explore good trade-offs between the true model and approximations. Our study highlights the interesting family of models that are beneficial to fit with missing values depending on the amount of data available.","url_abs":"https://arxiv.org/abs/2002.00658v2","url_pdf":"https://arxiv.org/pdf/2002.00658v2.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":"linear-predictor-on-linearly-generated-data","repo_url":"https://github.com/marineLM/linear_predictor_missing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"generalization-bounds","task_name":"Generalization Bounds"},{"task_slug":"missing-values","task_name":"Missing Values"}],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.00658","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.00658"}},"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. 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