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Mathematics > Statistics Theory
Title: Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
(Submitted on 27 Mar 2024 (v1), last revised 12 Apr 2024 (this version, v2))
Abstract: This work analyzes the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can effectively recover the underlying subspace. It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.
Submission history
From: Teng Zhang [view email][v1] Wed, 27 Mar 2024 15:03:29 GMT (123kb)
[v2] Fri, 12 Apr 2024 20:06:24 GMT (43kb)
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