1.8 Kernel Ridge Regression via Smoothing Splines
Автор: Jingyuan Hu
Загружено: 2026-03-01
Просмотров: 47
Описание:
In the previous videos: smoothing splines via calculus of variations and differential equations.
This video: the same problem through linear algebra in function space.
• Operator formulation of the spline objective
• Inner products and Hilbert space structure
• Normal equation in function space
• Variational calculus and resulting ODE
• Infinite-dimensional vs finite-dimensional analogy
• Change of variables → ridge regression form
• Singular Value Decomposition (SVD)
• Kernel trick
• Kernel ridge regression
Main message:
Smoothing splines = kernel ridge regression.
Linear algebra in function space.
No basis assumptions. No special structure required.
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