Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

Understand

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc.

• This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks.
• Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class.
• Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation.