Author

Lei Shi

3 papers indexed here

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#machine learning Sep 2025

A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning

A stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels and vector-valued interpolation spaces is developed, thereby enabling rich structural modeling with rigorous theoretical guarantees.

Jia-Qi Yang, Lei Shi · arXiv.org · 1 citation

#machine learning Apr 2025

Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

This work considers 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 vector-valued reproducing kernel Hilbert space induced by an operator-valued kernel.

Jia-Qi Yang, Lei Shi · arXiv.org · 2 citations

#machine learning Preprint Feb 2024

Stochastic Gradient Descent for Operator Learning in Hilbert Spaces: Convergence Rates and Minimax Lower Bounds

This study investigates the use of stochastic gradient descent to learn operators between general Hilbert spaces and establishes upper bounds for convergence rates of the SGD algorithm and derives a minimax lower bound analysis, illustrating that convergence analysis and regularity conditions quantitatively characteriz...

Lei Shi, Jia-Qi Yang · 2 citations