Concept

Projection matrix

Related lectures (14)

Equivalent Degrees of Freedom in Spline Smoothing

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

Delves into linear regression, emphasizing least squares estimation, residuals, and variance.

Explores the construction and application of Hadamard matrices for efficient estimation of main effects without interactions in the Plackett-Burman Design.

Linear Regression Basics

Introduces the basics of linear regression, covering OLS approach, residuals, hat matrix, and Gauss-Markov assumptions.

Fluctuation-dissipation relations for reversible diffusions

Covers linear response, steady states, Girsanov transforms, and covariance limits in reversible diffusions.

Regression Methods: Model Building and Inference

Covers analysis of variance, model building, variable selection, and function estimation in regression methods.

Linear Regression: Basics and Geometric Interpretation

Explores Gaussian linear regression, design matrix, least squares estimation, and geometric interpretation in linear regression analysis.

Harmonic Signals and Spectrum Estimation

Explores harmonic signals, spectrum estimation, and signal analysis methods using MATLAB tools.

Gaussian Conditional Model and Properties

Explores the Gaussian conditional model for linear regression and the properties of Gaussian data, illustrated with the example of kidney stone treatment comparison.

Linear Regression Basics: ERM Perspective

Introduces linear regression basics from an empirical risk minimization perspective, covering the square loss, data preprocessing, and gradient computation.

Linear Regression: Maximum Likelihood Approach

Covers linear regression topics including confidence intervals, variance, and maximum likelihood approach.

Estimation Example: Least Square Estimation

Covers the concept of least square estimation and its real-world applications.

Solving the linear system: Iterative methods

Explores iterative methods for solving linear systems and multigrid concepts to improve accuracy and convergence.

Regression: Simple and Multiple Linear

Covers simple and multiple linear regression, including least squares estimation and model diagnostics.