Blind Polynomial Regression

Alberto Natali; Geert Leus

doi:10.1109/ICASSP49357.2023.10095361

Blind Polynomial Regression

Signal Processing Systems

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

Original language	English
Title of host publication	Proceedings of the ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Place of Publication	Piscataway
Publisher	IEEE
Number of pages	5
ISBN (Electronic)	978-1-7281-6327-7
ISBN (Print)	978-1-7281-6328-4
DOIs	https://doi.org/10.1109/ICASSP49357.2023.10095361
Publication status	Published - 2023
Event	48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023 - Rhodes Island, Greece Duration: 4 Jun 2023 → 10 Jun 2023

Conference

Conference	48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023
Abbreviated title	ICASSP 2023
Country/Territory	Greece
City	Rhodes Island
Period	4/06/23 → 10/06/23

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

polynomial regression
interpolation
Vandermonde
matrix factorization
MUSIC

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10.1109/ICASSP49357.2023.10095361

Blind Polynomial RegressionFinal published version, 836 KB

Cite this

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title = "Blind Polynomial Regression",

abstract = "Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.",

keywords = "polynomial regression, interpolation, Vandermonde, matrix factorization, MUSIC",

author = "Alberto Natali and Geert Leus",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; 48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023, ICASSP 2023 ; Conference date: 04-06-2023 Through 10-06-2023",

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AU - Natali, Alberto

AU - Leus, Geert

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2023

Y1 - 2023

N2 - Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

AB - Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

KW - polynomial regression

KW - interpolation

KW - Vandermonde

KW - matrix factorization

KW - MUSIC

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U2 - 10.1109/ICASSP49357.2023.10095361

DO - 10.1109/ICASSP49357.2023.10095361

M3 - Conference contribution

SN - 978-1-7281-6328-4

BT - Proceedings of the ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

PB - IEEE

CY - Piscataway

T2 - 48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023

Y2 - 4 June 2023 through 10 June 2023

ER -

Blind Polynomial Regression

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Keywords

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