2022/03/17 by Tyler Maunu, Maunu, Tyler, Chenyu Yu +3
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Artificial intelligence #Computer science #Cryptography and Security (cs.CR) #Economics #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Gradient descent #Image (mathematics) #Machine Learning (cs.LG) #Mathematical optimization #Mathematics #Noise (video) #Optimization and Control (math.OC) #Outlier #Robust statistics #Sparse and Compressive Sensing Techniques #Stochastic gradient descent #Stylized fact #Subspace topology #cs.CR #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.2203.09276
published in arXiv (Cornell University) (Cornell University) · 34 pages, 9 figures
arxiv created 2022/03/17 · openalex publication_date 2022/03/17 · arxiv updated 2022/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop theoretically guaranteed stochastic methods for outlier-robust PCA. Outlier-robust PCA seeks an underlying low-dimensional linear subspace from a dataset that is corrupted with outliers. We are able to show that our methods, which involve stochastic geodesic gradient descent over the Grassmannian manifold, converge and recover an underlying subspace in various regimes through the development of a novel convergence analysis. The main application of this method is an effective differentially private algorithm for outlier-robust PCA that uses a Gaussian noise mechanism within the stochastic gradient method. Our results emphasize the advantages of the nonconvex methods over another convex approach to solving this problem in the differentially private setting. Experiments on synthetic and stylized data verify these results.