Generalized Eigenvalue Problems with Generative Priors

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of GEPs and are widely used in statistical data processing. In this work, we study GEPs under generative priors, assuming that the underlying leading generalized eigenvector lies within the range of a Lipschitz continuous generative model. Under appropriate conditions, we show that any optimal solution to the corresponding optimization problems attains the optimal statistical rate. Moreover, from a computational perspective, we propose an iterative algorithm called the Projected Rayleigh Flow Method (PRFM) to approximate the optimal solution. We theoretically demonstrate that under suitable assumptions, PRFM converges linearly to an estimated vector that achieves the optimal statistical rate. Numerical results are provided to demonstrate the effectiveness of the proposed method.

Authors

• Zhaoqiang Liu University of Electronic Science and Technology of China
• Wen Li Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China School of Computer Science and Engineering, University of Electronic Science and Technology of China
• Junren Chen University of Hong Kong

Keywords

No keywords are indexed for this paper.