Concept

Spline (mathematics)

Related lectures (29)

Explores B-splines, natural cubic splines, and smoothing splines in regression problems and their practical applications.

Natural Cubic Splines: Optimization and Penalization

Explores the optimization and penalization of natural cubic splines, including roughness penalties and Bayesian inference.

Bezier Curves II

Covers Bezier curves, de Casteljau Algorithm, properties, derivatives, splines, and end-points.

Image Processing II: B-spline Properties and Gradient Operators

Explores B-spline properties, gradient operators, interpolation, and differentiation filters in image processing.

Piecewise Polynomial Interpolation: Splines

Covers piecewise polynomial interpolation with splines, focusing on Lagrange interpolation with Chebyshev nodes and error convergence.

Image Processing II

Explores image interpolation, splines, wavelets, and geometric transformations in image processing.

Nonlinear Equations: Interpolation and Error Analysis

Covers the interpolation of nonlinear functions using Lagrange polynomials and error analysis.

Splines and Imaging: From Compressed Sensing to Deep Neural Nets

Explores the optimality of splines for imaging and deep neural networks, demonstrating sparsity and global optimality with spline activations.

Image Processing II: Polynomial Splines

Explores spatial transformations, polynomial splines, B-spline properties, interpolation, and differential operators in image processing.

Splines: Least-Squares Method

Explores splines, emphasizing the least-squares method for interpolating splines and demonstrating its application using MATLAB.

Cubic Splines and Least-Squares Approximation

Explores cubic splines and least-squares approximation, focusing on interpolation methods and error analysis.

Piecewise Linear Interpolation and Spline Interpolation

Covers piecewise linear and spline interpolation methods, stability, convergence, and data interpolation using splines.

Spline Interpolation and Approximation

Explores spline interpolation, least-squares approximation, and error analysis in interpolation.

Equivalent Degrees of Freedom in Spline Smoothing

Explores equivalent degrees of freedom in spline smoothing and the bias-variance tradeoff in fitting data.

Spline Interpolation: Definition and Error Analysis

Explains spline interpolation and error analysis in approximating data points using piecewise linear and spline methods.

Regression Methods: Spline Smoothing

Covers regression methods focusing on spline smoothing and penalised fitting to balance data fidelity and smoothness.

Piecewise Linear Interpolation

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

More on Splines: Penalised Likelihood and Natural Cubic Splines

Explores penalised likelihood and natural cubic splines, showcasing the unique explicit solution and the optimality of spline interpolation.

Deep Splines: Unifying Framework for Deep Neural Networks

Introduces a functional framework for deep neural networks with adaptive piecewise-linear splines, focusing on biomedical image reconstruction and the challenges of deep splines.

Transformations of Input or Output

Covers handling missing data, feature engineering, and output transformations in machine learning.