Mathematics of Data: Models and Estimators

This lecture introduces the Mathematics of Data, focusing on data models, optimization formulations, numerical algorithms, and analysis techniques to extract information from data while considering trade-offs. It covers machine learning paradigms, statistical learning, and the role of models and data in empirical risk minimization. The instructor discusses the importance of loss functions, estimators, and the ML approach in various scenarios, such as quantum tomography and linear models. Practical issues like performance evaluation, overfitting, and the comparison between ML and James-Stein estimators are also addressed.