{"paper":{"title":"Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Alejandra Castillo, Alona Kryshchenko, Deanna Needell, Iryna Hartsock, Jamie Haddock, Kamila Larripa, Karamatou Yacoubou Djima, Lara Kassab, Paulina Hoyos, Shambhavi Suryanarayanan","submitted_at":"2025-03-23T20:15:33Z","abstract_excerpt":"The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we address the tensor linear system problem $\\mathcal{A} \\mathcal{X}=\\mathcal{B}$, where $\\mathcal{A}$ is a measurement operator, $\\mathcal{X}$ is the unknown tensor-valued signal, and $\\mathcal{B}$ contains the measurements, possibly corrupted by arbitrary errors. Such corruption is common in large-scale tensor data, where transmission, sensory, or storage errors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18190","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.18190/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}