Linear Algebra in Data Science

This lecture covers the application of elementary linear algebra in data science, focusing on the use of active variables and orthogonal decomposition. The instructor explains the concept of weights in reducing variance and increasing variable influence in least squares. The lecture also delves into the distribution theory of linear models, the sufficiency of estimators, and the unbiasedness of estimates. Additionally, it explores the independence of estimators and the conditional distributions of variables, emphasizing the importance of sufficient statistics. The session concludes with a discussion on the expected value of estimators and the conditions for maximum likelihood estimates in statistical modeling.