On denoising modulo 1 samples of a function
Consider an unknown smooth function f : [0, 1] → R, and say we are given n noisy mod 1 samples of f, i.e., yi = (f(xi) + ηi) mod 1 for xi ∈ [0, 1], where ηi denotes noise. Given the samples (xi , yi) n i=1 our goal is to recover smooth, robust estimates of the clean samples f(xi) mod 1. We formulate...
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| Format: | Conference item |
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Proceedings of Machine Learning Research
2018
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| _version_ | 1826302852076666880 |
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| author | Cucuringu, M Tyagi, H |
| author_facet | Cucuringu, M Tyagi, H |
| author_sort | Cucuringu, M |
| collection | OXFORD |
| description | Consider an unknown smooth function f : [0, 1] → R, and say we are given n noisy mod 1 samples of f, i.e., yi = (f(xi) + ηi) mod 1 for xi ∈ [0, 1], where ηi denotes noise. Given the samples (xi , yi) n i=1 our goal is to recover smooth, robust estimates of the clean samples f(xi) mod 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 the unit circle. Our proposed approach is based on solving its relaxation which is a trust region subproblem, and hence solvable efficiently. We demonstrate its robustness to noise via extensive simulations on several synthetic examples, and provide a detailed theoretical analysis. |
| first_indexed | 2024-03-07T05:53:42Z |
| format | Conference item |
| id | oxford-uuid:e9ca584e-2a74-4169-80ce-c7887ae3bf8f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:53:42Z |
| publishDate | 2018 |
| publisher | Proceedings of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:e9ca584e-2a74-4169-80ce-c7887ae3bf8f2022-03-27T10:56:51ZOn denoising modulo 1 samples of a functionConference itemhttp://purl.org/coar/resource_type/c_1843uuid:e9ca584e-2a74-4169-80ce-c7887ae3bf8fSymplectic Elements at OxfordProceedings of Machine Learning Research2018Cucuringu, MTyagi, HConsider an unknown smooth function f : [0, 1] → R, and say we are given n noisy mod 1 samples of f, i.e., yi = (f(xi) + ηi) mod 1 for xi ∈ [0, 1], where ηi denotes noise. Given the samples (xi , yi) n i=1 our goal is to recover smooth, robust estimates of the clean samples f(xi) mod 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 the unit circle. Our proposed approach is based on solving its relaxation which is a trust region subproblem, and hence solvable efficiently. We demonstrate its robustness to noise via extensive simulations on several synthetic examples, and provide a detailed theoretical analysis. |
| spellingShingle | Cucuringu, M Tyagi, H On denoising modulo 1 samples of a function |
| title | On denoising modulo 1 samples of a function |
| title_full | On denoising modulo 1 samples of a function |
| title_fullStr | On denoising modulo 1 samples of a function |
| title_full_unstemmed | On denoising modulo 1 samples of a function |
| title_short | On denoising modulo 1 samples of a function |
| title_sort | on denoising modulo 1 samples of a function |
| work_keys_str_mv | AT cucuringum ondenoisingmodulo1samplesofafunction AT tyagih ondenoisingmodulo1samplesofafunction |