6 papers
Basic Inequalities for First-Order Optimization with Applications to Statistical Risk Analysis
Seunghoon Paik, Kangjie Zhou, Matus Telgarsky +1
We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularizat…
Which exceptional low-dimensional projections of a Gaussian point cloud can be found in polynomial time?
Andrea Montanari, Kangjie Zhou
Given -dimensional standard Gaussian vectors , we consider the set of all empirical distributions of its -dimensional projections, f…
Implicit Bias of Gradient Descent for Non-Homogeneous Deep Networks
Yuhang Cai, Kangjie Zhou, Jingfeng Wu +3
We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key propert…
Dynamic Factor Analysis of High-dimensional Recurrent Events
Fangyi Chen, Yunxiao Chen, Zhiliang Ying +1
Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving many ev…
Sharp Analysis of Power Iteration for Tensor PCA
Yuchen Wu, Kangjie Zhou
We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is…
A statistical theory of overfitting for imbalanced classification
Jingyang Lyu, Kangjie Zhou, Yiqiao Zhong
Classification with imbalanced data is a common challenge in data analysis, where certain classes (minority classes) account for a small fraction of the training data compared with…