Linear Models for Classification: Logistic Regression and SVM

This lecture focuses on linear models for classification, transitioning from regression concepts. It begins with a recap of linear regression, introducing the loss function and empirical risk. The instructor explains how to apply linear models to classification tasks, specifically through logistic regression. The logistic function is introduced as a means to convert continuous outputs into discrete labels, addressing the limitations of least squares for classification. The decision boundary concept is discussed, illustrating how it changes with new data points. The lecture also covers the support vector machine (SVM) approach, emphasizing margin maximization and the role of support vectors in determining the decision boundary. The differences between logistic regression and SVM are highlighted, particularly in their loss functions and sensitivity to outliers. The session concludes with a discussion on the practical implications of these models in machine learning, reinforcing the importance of understanding loss functions and decision boundaries in classification tasks.