Thresholding Based Efficient Outlier Robust PCA

Transcript:Thresholding Based Efficient Outlier Robust PCA:
Thresholding Based Efficient Outlier Robust PCA Yeshwanth Cherapanamjeri, Prateek Jain, Praneeth Netrapalli Microsoft Research India Vanilla PCA Vanilla PCA Outlier Robust PCA Our Contributions Outlier Effects – Blatant Outliers Outliers with large contribution Outlier Effects – Subtle Outliers Outlier with small contribution to principal subspace Earlier strategy doesn’t work Outlier Effects – Subtle Outliers Outliers generally have larger residual than inliers Algorithm (TORP) Threshold Points Algorithm (TORP) Threshold Points Algorithm (TORP) Theorem - Noiseless Case Theorem - Noiseless Case Theorem - Noisy Case Theorem - Noisy Case Prior Work Theorem Gaussian Case Prior Work (Gaussian Noise Case) Application to Anomaly Detection Given a set of URLs, separate good from bad Hypothesis: Good ones belong to a low dimensional space Results: Conclusions Thank You Algorithm – First Pass Algorithm 1 – Coherence Based Thresholding Adversarial Example Adversarial Example – Iteration 1 Adversarial Example – Iteration 2 Adversarial Example – Contd Proof Overview Proof Overview Proof of Theorem Proof of Theorem Appendix and Extra Slides Convex Relaxation (Outlier Pursuit) Theorem - TORP