Estimation and Detection

This lecture discusses the concepts of estimation and detection, highlighting the difference between regression and classification in machine learning. It explains how having a probabilistic model provides more information for the task, leading to optimal ways of performing regression and classification. The instructor covers topics such as learning probability distributions, joint probability distribution, linear estimation, and squared norm distortion. The lecture delves into the process of estimating a quantity D based on observations X, emphasizing the importance of choosing a good estimator and defining a cost function. It also explores the concept of linear estimators and the orthogonality principle in finding the optimal choice for estimation. The lecture concludes with a discussion on the relationship between Hilbert spaces, linear models, and the projection onto a space represented by W.