High Dimensional Robust Sparse Regression
summary
Shows that under i.i.d. Gaussian covariates and a k-sparse coefficient, a constant fraction epsilon of adversarial X and y outliers can be tolerated by combining iterative hard thresholding with a robust sparse gradient estimator; with an ellipsoid-based robust sparse mean routine the method attains near 50% breakdown and exact recovery when measurement noise sigma=0, needing about k^2 log D samples, and a faster order-D faster filtering variant trades worse epsilon dependence for runtime; sparse PCA relaxations and trimming/downweighting are the main tools.
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chapters (5)
- 0:00Start
- 17:28Problem setup for robust sparse regression
- 21:39Approach
- 27:16Key Ideas for Robust Mean/Covariance Estimation
- 43:05Theoretical results based on ellipsoid algorithm
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