论文标题
随机和私人非Convex Outier-bobust PCA
Stochastic and Private Nonconvex Outlier-Robust PCA
论文作者
论文摘要
我们开发了理论上保证了用于异常生动PCA的随机方法。 Outier-RobustCA从数据集中寻求基本的低维线性子空间，该数据集被异常值损坏。我们能够证明我们的方法涉及格拉斯曼尼亚歧管上的随机地球梯度下降，通过开发新的收敛分析来融合和恢复各种方案中的基本子空间。该方法的主要应用是一种有效的不同私有算法，用于在随机梯度方法中使用高斯噪声机理的异常值PCA。我们的结果强调了非Convex方法的优势，而不是在差异化私有环境中解决此问题的另一种凸方法。关于合成和程式化数据的实验验证了这些结果。
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.
