Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can be reformulated as one of approximating a high dimensional function from limited information available, such as a small number of samples. In general, this problem is known to suffer from the curse of dimensionality – the number of samples required to achieve a certain accuracy in the function reconstruction typically scales exponentially with the number of parameters. Modern approaches bypass this issue by making additional structural assumptions on the function such as: low intrinsic dimensionality, partial separability, sparse representations in a basis etc. This has led to a number of results over the past decade, leading to a rich theory, for many interesting models.
The workshop will focus on the mathematical foundations of this problem, featuring talks by eminent researchers in the fields of multivariate approximation theory, high-dimensional integration, non-parametric regression and related areas.
