Generalization Theory

This lecture covers the concept of generalization theory in machine learning, focusing on the challenges faced by data-based methods for inference and learning in higher-dimensional spaces. The curse of dimensionality is discussed, illustrating how the sample density varies with the dimension values. The lecture also delves into empirical risk minimization, Vapnik-Chervonenkis bound, PAC learning, and the bias-variance tradeoff. The instructor explains the relationship between bias and variance as model complexity increases, emphasizing the importance of finding a balance to avoid underfitting or overfitting.