Practical Aspects of Gaussian Linear Model

This lecture delves into the practical aspects of the Gaussian linear model, focusing on variable selection, minimizing prediction error, and dealing with interpretability issues arising from highly correlated features. The instructor explains methods to detect multicollinearity, such as using the condition number and variance inflation factor. The lecture covers techniques like rotating the data matrix and introducing regularization through Tikhonov regularization to control parameter values. Ridge regression is discussed as a method to stabilize the model by adding a penalty term to the least squares estimation, leading to a more interpretable and stable solution. The lecture concludes by exploring the bias and variance trade-off in ridge regression, highlighting how the choice of regularization parameter impacts the estimation of coefficients.