{"paper":{"title":"Monte Carlo integration of non-differentiable functions on $[0,1]^\\iota$, $\\iota=1,\\dots,d$, using a single determinantal point pattern defined on $[0,1]^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.CA","math.NA","math.ST","stat.TH"],"primary_cat":"stat.CO","authors_text":"Adrien Mazoyer, Jean-Fran\\c{c}ois Coeurjolly, Pierre-Olivier Amblard","submitted_at":"2020-02-28T15:07:55Z","abstract_excerpt":"This paper concerns the use of a particular class of determinantal point processes (DPP), a class of repulsive spatial point processes, for Monte Carlo integration. Let $d\\ge 1$, $I\\subseteq \\overline d=\\{1,\\dots,d\\}$ with $\\iota=|I|$. Using a single set of $N$ quadrature points $\\{u_1,\\dots,u_N\\}$ defined, once for all, in dimension $d$ from the realization of the DPP model, we investigate \"minimal\" assumptions on the integrand in order to obtain unbiased Monte Carlo estimates of $\\mu(f_I)=\\int_{[0,1]^\\iota} f_I(u) \\mathrm{d} u$ for any known $\\iota$-dimensional integrable function on $[0,1]^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.10323","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.10323/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"}