11 papers
Feature Learning for the High Dimensional Stationary Schödinger Equation with Deep Ritz Method
Yao Yao, Yulong Lu, Gilad Lerman
This paper investigates feature learning within the framework of the deep Ritz method for solving the stationary Schrödinger equation with Neumann boundary conditions. We first an…
Geometry-Preserving Encoder/Decoder in Latent Generative Models
Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou +2
Generative modeling aims to generate new data samples that resemble a given dataset. When using diffusion models for this task, one of the main challenges is solving the problem in…
The Sharp Phase Transition of Tyler's M-Estimator for Robust Subspace Recovery
Gilad Lerman, Teng Zhang
Robust Subspace Recovery (RSR) aims to identify an underlying d-dimensional subspace from a dataset heavily corrupted by outliers. Complexity-theoretic results establish a threshol…
QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition
Daniel Miao, Gilad Lerman, Joe Kileel
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and…
Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
Gilad Lerman, Kang Li, Tyler Maunu +1
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective appr…
Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
Gilad Lerman, Teng Zhang
This work analyzes the subspace-constrained Tyler's estimator (STE), a method designed to recover a low-dimensional subspace from a dataset that may be heavily corrupted by outlier…