Wahba problem in spline smoothing

E933493

nonparametric regression method smoothing spline formulation statistical optimization problem

The Wahba problem in spline smoothing is a foundational statistical formulation that determines an optimal smoothing spline by balancing data fidelity with smoothness, widely used in nonparametric regression and curve fitting.

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Statements (49)

Predicate	Object
instanceOf	nonparametric regression method ⓘ smoothing spline formulation ⓘ statistical optimization problem ⓘ
appliedIn	geostatistics ⓘ machine learning regression tasks ⓘ signal processing ⓘ statistics ⓘ
associatedWith	Wahba, 1990, Spline Models for Observational Data NERFINISHED ⓘ
assumes	additive noise model ⓘ square-integrable underlying function ⓘ
basedOn	penalized least squares ⓘ
computationalMethod	eigendecomposition of smoothing matrix ⓘ linear system solution ⓘ
criterionForm	sum of squared residuals plus lambda times roughness penalty ⓘ
dataType	noisy observations of an unknown function ⓘ
field	machine learning ⓘ numerical analysis ⓘ statistics ⓘ
hasComponent	data misfit term ⓘ roughness penalty term ⓘ
influenced	development of kernel smoothing methods ⓘ smoothing spline ANOVA models ⓘ
introducedBy	Grace Wahba NERFINISHED ⓘ
involvesParameter	smoothing parameter ⓘ
mathematicalSetting	reproducing kernel Hilbert space ⓘ variational problem ⓘ
objective	balance data fidelity and smoothness ⓘ minimize penalized residual sum of squares ⓘ
optimizationType	convex optimization problem ⓘ
output	smoothing spline estimator ⓘ
relatedConcept	Gaussian process regression NERFINISHED ⓘ Tikhonov regularization NERFINISHED ⓘ kernel methods ⓘ regularization theory ⓘ ridge regression ⓘ
smoothingParameterRole	controls tradeoff between fit and smoothness ⓘ
solutionProperty	unique minimizer under standard conditions ⓘ
solutionType	natural cubic smoothing spline in one dimension ⓘ thin plate spline in multiple dimensions ⓘ
timePeriod	late 20th century ⓘ
typicalPenalty	Sobolev norm of the function ⓘ integrated squared second derivative ⓘ
usedFor	curve fitting ⓘ function estimation from noisy data ⓘ nonparametric regression ⓘ signal smoothing ⓘ spline smoothing ⓘ surface smoothing ⓘ time series smoothing ⓘ

Referenced by (1)

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Grace Wahba → notableConcept → Wahba problem in spline smoothing ⓘ