{"paper":{"title":"Near-Optimal and Tractable Estimation under Shift-Invariance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Dmitrii M. Ostrovskii","submitted_at":"2024-11-05T18:11:23Z","abstract_excerpt":"How hard is it to estimate a discrete-time signal $(x_{1}, ..., x_{n}) \\in \\mathbb{C}^n$ satisfying an unknown linear recurrence relation of order $s$ and observed in i.i.d. complex Gaussian noise? The class of all such signals is parametric but extremely rich: it contains all exponential polynomials over $\\mathbb{C}$ with total degree $s$, including harmonic oscillations with $s$ arbitrary frequencies. Geometrically, this class corresponds to the projection onto $\\mathbb{C}^{n}$ of the union of all shift-invariant subspaces of $\\mathbb{C}^\\mathbb{Z}$ of dimension $s$. We show that the statist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03383","kind":"arxiv","version":3},"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/2411.03383/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"}