Approximation and Learning with Tree Tensor Networks

Explore the world of tree tensor networks (TTNs) in this comprehensive lecture on approximation and learning techniques. Delve into the fundamentals of tensorization and TTNs, examining their approximation classes and properties. Discover how TTNs achieve optimal rates for a wide range of smoothness spaces without requiring adaptation to function regularity. Investigate the importance of deep networks with free depth and the benefits of exploiting tensor sparsity. Learn about the potential of tensor networks to handle functions beyond standard regularity classes. Examine learning aspects in a statistical setting, focusing on model selection strategies and minimax adaptive approaches in least-squares settings. Gain insights into balancing estimation and approximation errors when working with limited observations.