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Low-rank matrix recovery via nonconvex optimization methods with application to errors-in-variables matrix regression
Xin Li, Dongya Wu
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for an…
Adversarially robust generalization theory via Jacobian regularization for deep neural networks
Dongya Wu, Xin Li
Powerful deep neural networks are vulnerable to adversarial attacks. To obtain adversarially robust models, researchers have separately developed adversarial training and Jacobian…
Sparse deep neural networks for nonparametric estimation in high-dimensional sparse regression
Dongya Wu, Xin Li
Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is…
Low-rank matrix estimation via nonconvex spectral regularized methods in errors-in-variables matrix regression
Xin Li, Dongya Wu
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including mul…