{"paper":{"title":"A Bounded $p$-norm Approximation of Max-Convolution for Sub-Quadratic Bayesian Inference on Additive Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"stat.CO","authors_text":"Julianus Pfeuffer, Oliver Serang","submitted_at":"2015-05-28T01:03:29Z","abstract_excerpt":"Max-convolution is an important problem closely resembling standard convolution; as such, max-convolution occurs frequently across many fields. Here we extend the method with fastest known worst-case runtime, which can be applied to nonnegative vectors by numerically approximating the Chebyshev norm $\\| \\cdot \\|_\\infty$, and use this approach to derive two numerically stable methods based on the idea of computing $p$-norms via fast convolution: The first method proposed, with runtime in $O( k \\log(k) \\log(\\log(k)) )$ (which is less than $18 k \\log(k)$ for any vectors that can be practically re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07519","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}