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Given the samples $(x_i,y_i)_{i=1}^{n}$ our goal is to recover smooth, robust estimates of the clean samples $f(x_i) \\bmod 1$. We formulate a natural approach for solving this problem which works with representations of mod 1 values over the unit circle. This amounts to solving a quadratically constrained quadratic program (QCQP) with non-convex constraints involving points lying on"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.10210","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-27T15:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"e5c78efc7c60a9d9a4005234ffd1103af8d4838666067fb0d3c841122cb21799","abstract_canon_sha256":"69e2a31920e935dfc1fe6d3ff7e2993552fa5cc781287202644d8125c5a1c1b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:35.250377Z","signature_b64":"U/mpgWkqQlR7KzI+1fPufU1ns9M8P6Q+PNiXwcGEJPCCmzx+EZrYAqU9xyh5cmJlnDiNZLTnLaKeI4Kw89R3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ec308e74388305d60af012735746e6c767a1ed5a6888490a6129670acce7e61","last_reissued_at":"2026-05-18T00:19:35.249705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:35.249705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On denoising modulo 1 samples of a function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Hemant Tyagi, Mihai Cucuringu","submitted_at":"2017-10-27T15:55:50Z","abstract_excerpt":"Consider an unknown smooth function $f: [0,1] \\rightarrow \\mathbb{R}$, and say we are given $n$ noisy$\\mod 1$ samples of $f$, i.e., $y_i = (f(x_i) + \\eta_i)\\mod 1$ for $x_i \\in [0,1]$, where $\\eta_i$ denotes noise. 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