Σύγκριση μεθόδων
Εξετάστε τις επιλεγμένες μεθόδους δίπλα-δίπλα· οι γραμμές που διαφέρουν επισημαίνονται.
| Γενικευμένο Προσθετικό Μοντέλο (GAM)× | Τοπική Παλινδρόμηση LOESS / LOWESS× | Παλινδρομική Ανάλυση Πολυωνύμου× | |
|---|---|---|---|
| Πεδίο≠ | Μηχανική Μάθηση | Μηχανική Μάθηση | Στατιστική |
| Οικογένεια≠ | Machine learning | Machine learning | Regression model |
| Έτος προέλευσης≠ | 1986 | 1979 | 2012 |
| Δημιουργός≠ | Trevor Hastie & Robert Tibshirani | William S. Cleveland | Montgomery, Peck & Vining (textbook treatment); classical least squares |
| Τύπος≠ | Semi-parametric additive regression model | Local nonparametric regression smoother | Linear regression in transformed predictors |
| Θεμελιώδης πηγή≠ | Hastie, T., & Tibshirani, R. (1986). Generalized additive models. Statistical Science, 1(3), 297–310. 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 |
| Εναλλακτικές ονομασίες≠ | GAM, additive model, spline-based additive regression, Genelleştirilmiş toplamsal model | LOWESS, local regression, locally weighted scatterplot smoothing, yerel regresyon | polynomial least squares, curvilinear regression, Polinom Regresyonu |
| Συναφείς≠ | 4 | 3 | 4 |
| Σύνοψη≠ | A generalized additive model, introduced by Trevor Hastie and Robert Tibshirani in 1986, extends the generalized linear model by replacing each linear term with a smooth, data-driven function of the predictor. This lets the model capture nonlinear relationships while preserving the additive, term-by-term interpretability of regression: each predictor contributes its own estimated curve, and the curves simply add up (on a link scale) to predict the response. | 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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