Mathematics of Data: Data, Models, and Optimization

This lecture introduces the role of models and data in the context of maximum-likelihood formulations, focusing on sample complexity bounds for estimation and prediction. It covers topics such as empirical risk minimization, statistical learning, and optimization formulations, providing an overview of the Mathematics of Data course. The instructor discusses the importance of understanding trade-offs in extracting information and knowledge from data, presenting examples of statistical learning, including classification, regression, and density estimation problems.