Level Set Learning with Pseudo-Reversible Neural Networks for Nonlinear Dimension Reduction in Function Approximation
科研大讨论系列报告
报告题目(Title)：Level Set Learning with Pseudo-Reversible Neural Networks for Nonlinear Dimension Reduction in Function Approximation
报告人(Speaker)：Professor Lili Ju (University of South Carolina)
地点(Place)：后主楼1223
时间(Time)：2023年6月9日 (周五), 10:00-11:00
邀请人(Inviter)：蔡勇勇
报告摘要
Inspired by the Nonlinear Level set Learning (NLL) method that uses the reversible residual network (RevNet), we propose a new method of Dimension Reduction via Learning Level Sets (DRiLLS) for function approximation. Our method contains two major components: one is the pseudo-reversible neural network (PRNN) module that effectively transforms high-dimensional input variables to low-dimensional active variables, and the other is the synthesized regression module for approximating function values based on the transformed data in the low-dimensional space. The PRNN not only relaxes the invertibility constraint of the nonlinear transformation present in the NLL method due to the use of RevNet, but also adaptively weights the influence of each sample and controls the sensitivity of the function to the learned active variables. The synthesized regression uses Euclidean distance in the input space to select neighboring samples, whose projections on the space of active variables are used to perform local least-squares polynomial fitting. This helps to resolve numerical oscillation issues present in traditional local and global regressions. Extensive experimental results demonstrate that our DRiLLS method outperforms both the NLL and Active Subspace methods, especially when the target function possesses critical points in the interior of its input domain.
