Lecture

Linear Models: Least Squares and QR Factorization

Related lectures (29)

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

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Explores linear models, least squares, Gaussian vectors, and model selection methods.

Least Squares Solutions

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

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Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Matrix Equivalence Theorems

Explores matrix equivalence theorems for systems of equations and least squares solutions.

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Covers the basics of linear regression, including OLS, heteroskedasticity, autocorrelation, instrumental variables, Maximum Likelihood Estimation, time series analysis, and practical advice.

Linear Models: Ridge, OLS and LASSO

Covers linear models like Ridge, OLS, and LASSO, explaining singular values and regression analysis.

Linear Regression: Basics and Estimation

Covers the basics of linear regression and how to solve estimation problems using least squares and matrix notation.

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Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

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Discusses the geometry of least squares, exploring row and column perspectives, hyperplanes, projections, residuals, and unique vectors.

Likelihood Estimation and Least Squares

Introduces simple and multiple normal linear regression, and maximum likelihood estimation with practical examples.

Nonlinear Machine Learning: k-Nearest Neighbors and Feature Expansion

Covers the transition from linear to nonlinear models, focusing on k-NN and feature expansion techniques.

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Covers linear models for multi-class classification, focusing on logistic regression and evaluation metrics.

Linear Regression: Least Squares Method

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

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Regression: Linear Models

Explores linear regression, least squares, residuals, and confidence intervals in regression models.