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stat.ML2025
A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Jia-Qi Yang, Lei Shi
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework…
stat.ML2025
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Jia-Qi Yang, Lei Shi
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a v…