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This article aims to extend this methodology to the pairwise case, when the variable to be explained takes the form of a similarity function between two independent observations, such as pixelated ID photos, as input data of biometric systems) and the explanatory variables take the form of a pair of covariates of the observations, such as the age or the hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove genera","title":"On Pairwise Quantile Regression -- Statistical Guarantees and Applications","url":"https://arxiv.org/abs/2607.04431","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.04431v1 Announce Type: cross \nAbstract: Quantile regression provides a powerful tool for summarizing the conditional distribution of a real valued random variable (r.v.) of interest $Y$ as a function of covariates $Z$ in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise case, when the variable to be explained takes the form of a similarity function between two independent observations, such as pixelated ID photos, as input data of biometric systems) and the explanatory variables take the form of a pair of covariates of the observations, such as the age or the hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove genera","title":"On Pairwise Quantile Regression -- Statistical Guarantees and Applications","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-07T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.04431"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e162cd8bc5898aa06c1e0d72004b38b649330ddf9f7c70d2e79f85117111106026bd8bf458481153d7cb24e5f27a7fe9d733f2c5123e51bb5907467cd6d65805","signer":"crovia.substrate","subject":{"observed_at":"2026-07-07T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.04431"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"b8fcaf9b0c17ac341b6bc1dd13e07b6a2db8a6cfdbfa5523035f20175fd84382","leaf_index":289053,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"c19cdb8f54a1a89c40cd823a0fb7bfa8bbc26a2b722c3d58411c629b59c3179c","side":"left"},{"sibling":"8f262ff37a1091d8ef84d33d67d3c6d6d7d02f60d55f70e57de5a56322b5f602","side":"right"},{"sibling":"f56139108af85accdf4c3934bcb713bfa7ecfabf46bfeffced4bea75606aaa88","side":"left"},{"sibling":"c3d11855581a197eb52072dd3cc13e1b48e2880616932d397a78cf73a73bd5f5","side":"left"},{"sibling":"416e6a8d29d0ec7cfded59d0a586154f03aca0ae8f66a6d69319669d52ee62e7","side":"left"},{"sibling":"e924b69c50c87915e35c49c68162276635ed10e79f8c56b2fb86e53e0967805f","side":"right"},{"sibling":"c3e53593f0d15a00effd5c8c5a5e631e06f64f32896f73801edae507488da3ab","side":"right"},{"sibling":"3b53d97c225577b0a2d53eeb1ca093f0c3441edf0f64e622c325f18db4fae31c","side":"right"},{"sibling":"35d3e8088ee93171aa479055dcd001cfb6d23925114ddc0908531e54298b0d29","side":"left"},{"sibling":"841129c21a7583176cdc7de281cadfe0e00d04673461e199760cd5128d8cc2d5","side":"right"},{"sibling":"19d6dfd29bc47f35fa02e8fe765277ba9cc3e6da5072309f24ebaac5b5f295e3","side":"right"},{"sibling":"8e0ad7889eb2d4b40e5b6c3d8e2eb19d4e202374983f468aa76321823de07a9f","side":"left"},{"sibling":"aae716235efcb893a1f219dbcd5095070d08a497769fc6d50c14976aa26d5750","side":"right"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"1b72ad8d12164fdf329e7871711be99d8569d140b21f94056e6962da21da9ce1","side":"right"},{"sibling":"5f5109c2bfdcc7a7e70554bba25862e2d7ce86b6b0cd48a72eb66d2eb735f321","side":"right"},{"sibling":"05fd8a05dddb2e7f72bbb5b290ca55c378f1aed709f132277908d9a5f30eb605","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":289613,"merkle_root":"dc428b9d9ba248d4f93f63147bf7c700bf5be7f500cec6c3507b9df6e9401601","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260707T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-07T05:38:15Z","sig_algorithm":"ed25519","signature":"c468b0e183383ab71992be40bda451093e6cd8cd8efb0d26f68e135a804b287c209d12a0f4fdd95c69c835c04b78df8cb1903dee1f53d4730b36f5332a29fe05","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_51e602979b1bbc53ecfa1c83deb2a6d88bd0cc1d160fbb5bfde95602834bf758"}}