On denoising modulo 1 samples of a function

Mihai Cucuringu, Hemant Tyagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 x∈ [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 angular embeddings of the noisy mod 1 samples over the unit complex circle, inspired by the angular synchronization framework. Our approach amounts to solving a quadratically constrained quadratic program (QCQP) which is NP-hard in its basic form, and therefore we consider its relaxation which is a trust region sub-problem and hence solvable efficiently. We demonstrate its robustness to noise via extensive numerical simulations on several synthetic examples, along with a detailed theoretical analysis. To the best of our knowledge, we provide the first algorithm for denoising mod 1 samples of a smooth function, which comes with robustness guarantees.
Original languageEnglish
Title of host publicationProceedings of Machine Learning Research
Number of pages25
Publication statusPublished - 9 Apr 2018
EventThe 21st International Conference on Artificial Intelligence and Statistics - Playa Blanca, Lanzarote, Canary Islands, Lanzarote, Spain
Duration: 9 Apr 201811 Apr 2018
Conference number: 21


ConferenceThe 21st International Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS 2018
Internet address


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