Mathematical Conversations

In this (short and informal) talk I will present the three fundamental factors that determine the quality of a statistical machine learning algorithm. I will then depict a classic strategy for handling these factors, which is relatively well understood, and until recently still gave rise to competitive results in practice. Finally, we will turn to discuss a radically different approach that in the last five years has revolutionized the world of machine learning. This approach, known as "deep learning", requires rethinking the foundations of statistical learning theory. The current state of our understanding, as well as many conjectures and open problems, will be outlined.