{"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/is-the-performance-of-my-deep-network-too","title":"Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification","arxiv_id":"2202.00395","date":"2022-02-01","proceeding":null,"authors":["Takashi Ishida","Ikko Yamane","Nontawat Charoenphakdee","Gang Niu","Masashi Sugiyama"],"abstract":"There is a fundamental limitation in the prediction performance that a machine learning model can achieve due to the inevitable uncertainty of the prediction target. In classification problems, this can be characterized by the Bayes error, which is the best achievable error with any classifier. The Bayes error can be used as a criterion to evaluate classifiers with state-of-the-art performance and can be used to detect test set overfitting. We propose a simple and direct Bayes error estimator, where we just take the mean of the labels that show \\emph{uncertainty} of the class assignments. Our flexible approach enables us to perform Bayes error estimation even for weakly supervised data. In contrast to others, our method is model-free and even instance-free. Moreover, it has no hyperparameters and gives a more accurate estimate of the Bayes error than several baselines empirically. Experiments using our method suggest that recently proposed deep networks such as the Vision Transformer may have reached, or is about to reach, the Bayes error for benchmark datasets. Finally, we discuss how we can study the inherent difficulty of the acceptance/rejection decision for scientific articles, by estimating the Bayes error of the ICLR papers from 2017 to 2023.","url_abs":"https://arxiv.org/abs/2202.00395v2","url_pdf":"https://arxiv.org/pdf/2202.00395v2.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":"is-the-performance-of-my-deep-network-too","repo_url":"https://github.com/takashiishida/irreducible","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"articles","task_name":"Articles"},{"task_slug":"binary-classification","task_name":"Binary Classification"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"},{"method_slug":"vision-transformer","method_name":"Vision Transformer"}],"datasets_introduced":[{"slug":"fashion-mnist-h","name":"Fashion-MNIST-H","full_name":""}],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2202.00395","atlas_url":"https://app.syntology.ai/?focus=2202.00395","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2202.00395"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/takashiishida/irreducible","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"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":1,"samples":[{"code_sha256_prefix":"4e3d0511afa06c49","entry":"main","repo":"takashiishida/irreducible","repo_kind":"official","path":"be_iclr.py","file_url":"https://github.com/takashiishida/irreducible/blob/HEAD/be_iclr.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"4e3d0511afa06c49"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}