Trade-offs in Data and Time

This lecture discusses the trade-offs between data and time in computational problems, emphasizing the joint treatment of data and computational aspects. It explores how numerical methods take longer for extra accuracy, while statistical models become more precise with more data. The lecture delves into the concept of diminishing returns in time and data efforts, presenting a continuous trade-off between using more data to make algorithms faster or vice versa. It also covers fundamental trade-offs in geometry, focusing on the intersection of convex bodies to understand optimization problems. The instructor explains the descent cone concept, illustrating how directions in this cone can decrease the objective function. The lecture concludes with a break before diving deeper into the topic.