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1.5 Multi-Dimensional Splines
In this video, we extend smoothing splines to the multidimensional setting. We move from the one-dimensional construction to the thin-plate spline framework and derive the full solution structure.
Watch the full series: https://www.youtube.com/playlist?list=PLdMM2W7mxqIYDURvh37jLz8sd8sDjonk5
0:00 — Goal
9:59 — Variational PDE
23:23 — Laplacian Operator
33:06 — Linear System
38:58— Summary
Topics:
• Multidimensional splines
• Smoothing splines
• Thin-plate splines
• Variational calculus
• Euler–Lagrange equation
• Partial differential equations (PDE)
• Curvature penalty
• Biharmonic operator
• Kernel methods
• Radial basis function (RBF)
• Representer theorem
• Kernel solution
• Penalized regression
• Linear system formulation
Видео 1.5 Multi-Dimensional Splines канала Jingyuan Hu
Watch the full series: https://www.youtube.com/playlist?list=PLdMM2W7mxqIYDURvh37jLz8sd8sDjonk5
0:00 — Goal
9:59 — Variational PDE
23:23 — Laplacian Operator
33:06 — Linear System
38:58— Summary
Topics:
• Multidimensional splines
• Smoothing splines
• Thin-plate splines
• Variational calculus
• Euler–Lagrange equation
• Partial differential equations (PDE)
• Curvature penalty
• Biharmonic operator
• Kernel methods
• Radial basis function (RBF)
• Representer theorem
• Kernel solution
• Penalized regression
• Linear system formulation
Видео 1.5 Multi-Dimensional Splines канала Jingyuan Hu
multidimensional splines smoothing splines thin plate splines variational calculus euler lagrange equation partial differential equations biharmonic equation laplacian operator delta function kernel methods RBF kernel penalized regression statistical learning machine learning math applied mathematics
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26 февраля 2026 г. 7:14:32
00:44:52
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