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.