1.8 Kernel Ridge Regression via Smoothing Splines скачать в хорошем качестве

1.8 Kernel Ridge Regression via Smoothing Splines

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.