A SIEVE STOCHASTIC GRADIENT DESCENT ESTIMATOR FOR ONLINE NONPARAMETRIC REGRESSION IN SOBOLEV ELLIPSOIDS.
Ann Stat
; 50(5): 2848-2871, 2022 Oct.
Article
en En
| MEDLINE
| ID: mdl-38169958
ABSTRACT
The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. in nonparametric regression, one assumes that the regression function belongs to a pre-specified infinite-dimensional function space (the hypothesis space). in the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly. inspired by nonparametric sieve estimation and stochastic approximation methods, we propose a sieve stochastic gradient descent estimator (Sieve-SGD) when the hypothesis space is a Sobolev ellipsoid. We show that Sieve-SGD has rate-optimal mean squared error (MSE) under a set of simple and direct conditions. The proposed estimator can be constructed with a low computational (time and space) expense We also formally show that Sieve-SGD requires almost minimal memory usage among all statistically rate-optimal estimators.
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Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
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En
Revista:
Ann Stat
Año:
2022
Tipo del documento:
Article