Approximation, sampling and compression in data science
Cambridge University
Programme Theme Approximation theory is the study of simulating potentially extremely complicated functions, called target functions, with simpler, more easily computable functions called approximants. The purpose of the simulation could be to approximate values of the target function with respect to a given norm, to estimate the integral of the target function, or to compute its minimum value. Approximation theory's relationship with computer science and engineering encourages solutions that are efficient with regards to computation time and space. In addition, approximation theory problems may also deal with real-life restrictions on data, which can be incomplete, expensive, or noisy. As a result, approximation theory often overlaps with sampling and compression problems.The main aim of this programme is to understand and solve challenging problems in the high-dimensional context, but this aim is dual. On one hand, we would like to use the high-dimensional context to underst