- 7 Moving Beyond Linearity 289
- 7.1 Polynomial Regression . . . . . . . . . . . . . . . . . . . . . 290
- 7.2 Step Functions . . . . . . . . . . . . . . . . . . . . . . . . . 292
- 7.3 Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . 293
- 7.4 Regression Splines . . . . . . . . . . . . . . . . . . . . . . . 294
- 7.4.1 Piecewise Polynomials . . . . . . . . . . . . . . . . 294
- 7.4.2 Constraints and Splines . . . . . . . . . . . . . . . 296
- 7.4.3 The Spline Basis Representation . . . . . . . . . . 296
- 7.4.4 Choosing the Number and Locations of the Knots . . . . . . 297
- 7.4.5 Comparison to Polynomial Regression . . . . . . . 299
- 7.5 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . . 300
- 7.5.1 An Overview of Smoothing Splines . . . . . . . . . 300
- 7.5.2 Choosing the Smoothing Parameter λ. . . . . . . 301
- 7.6 Local Regression . . . . . . . . . . . . . . . . . . . . . . . . 303
- 7.7 Generalized Additive Models . . . . . . . . . . . . . . . . . 305
- 7.7.1 GAMs for Regression Problems . . . . . . . . . . . 306
- 7.7.2 GAMs for Classification Problems . . . . . . . . . . 308
- 7.8 Lab: Non-Linear Modeling . . . . . . . . . . . . . . . . . . 309
- 7.8.1 Polynomial Regression and Step Functions . . . . . 310
- 7.8.2 Splines . . . . . . . . . . . . . . . . . . . . . . . . . 315
- 7.8.3 Smoothing Splines and GAMs . . . . . . . . . . . . 317
- 7.8.4 Local Regression . . . . . . . . . . . . . . . . . . . 324
- 7.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
TL;DR - Beyond Linearity
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Citation
BibTeX citation:
@online{bochman2024,
author = {Bochman, Oren},
title = {Chapter 7: {Moving} {Beyond} {Linearity}},
date = {2024-07-28},
url = {https://orenbochman.github.io/notes-islr/posts/ch07/},
langid = {en}
}
For attribution, please cite this work as:
Bochman, Oren. 2024. “Chapter 7: Moving Beyond Linearity.”
July 28, 2024. https://orenbochman.github.io/notes-islr/posts/ch07/.