Mathematical Statistics Seminar

Anthony Nouy, École Centrale Nantes

Learning high-dimensional functions with tree tensor networks

Tensor methods are among the most prominent tools for the approximation of high- dimensional functions. Such approximation problems naturally arise in statistical learning, stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high- dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we give an introduction to tree-based (hierarchical) tensor formats, which can be interpreted as deep neural networks with particular architectures. Then we present adaptive algorithms for the approximation in these formats using statistical methods.

Speakers

Anthony Nouy, École Centrale Nantes