Probabilistic Interpretation: Maximum Likelihood

This lecture explores an alternative route to the least-squares problem by starting from a probabilistic perspective, providing a second interpretation of the problem. It delves into Gaussian distribution, independence, and the density of random variables. The concept of Gaussian random vector with mean and covariance is discussed, along with the definition of a Gaussian random variable. The lecture also covers the concept of maximum likelihood estimation, regularization techniques like Ridge Regression and Lasso, and the importance of simplicity in model design. The implications of overfitting and underfitting are explained through examples and the use of different norms for regularization.