Porovnať metódy
Prezrite si vybrané metódy vedľa seba; riadky, ktoré sa líšia, sú zvýraznené.
| Regresné a vyhladzovacie splajny× | Lokálna regresia LOESS / LOWESS× | Polynomiálna regresia× | |
|---|---|---|---|
| Odbor≠ | Strojové učenie | Strojové učenie | Štatistika |
| Rodina≠ | Machine learning | Machine learning | Regression model |
| Rok vzniku≠ | 1996 | 1979 | 2012 |
| Tvorca≠ | Spline regression literature; P-splines by Eilers & Marx | William S. Cleveland | Montgomery, Peck & Vining (textbook treatment); classical least squares |
| Typ≠ | Piecewise-polynomial nonparametric regression | Local nonparametric regression smoother | Linear regression in transformed predictors |
| Pôvodný zdroj≠ | Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121. DOI ↗ | Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829–836. DOI ↗ | Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811 |
| Ďalšie názvy≠ | splines, cubic splines, natural splines, smoothing splines | LOWESS, local regression, locally weighted scatterplot smoothing, yerel regresyon | polynomial least squares, curvilinear regression, Polinom Regresyonu |
| Príbuzné≠ | 4 | 3 | 4 |
| Zhrnutie≠ | Regression splines model a nonlinear relationship by fitting piecewise polynomials that join smoothly at a set of points called knots. Cubic and natural splines are the most common, and smoothing splines add a roughness penalty that automatically balances fit against smoothness. Splines are the standard flexible building block for univariate nonlinear regression and the basis of generalized additive models. | LOESS (locally estimated scatterplot smoothing), introduced by William Cleveland in 1979 and extended with Susan Devlin in 1988, fits a smooth curve through data by performing a separate weighted polynomial regression in the neighbourhood of each point. Nearby observations count more than distant ones, so the method follows local structure without assuming any global functional form, making it a popular exploratory smoother for scatterplots. | Polynomial regression is a regression method that models non-linear relationships by including squared and higher-degree terms of an explanatory variable, and it is a core tool of response surface analysis. As developed in Montgomery, Peck and Vining's Introduction to Linear Regression Analysis (2012), it remains linear in its parameters even though the fitted curve bends. |
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