{"paper":{"title":"Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","quant-ph","stat.ML"],"primary_cat":"cs.IT","authors_text":"Nir Weinberger, Sreejith Sreekumar","submitted_at":"2026-02-20T17:16:38Z","abstract_excerpt":"Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states. We provide an interpretation of this predictor in terms of quantum reverse information projection and quantum Pythagorean theorem when t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.18364","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/2602.18364/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"}