A poly-time algorithm achieves O(β)^{o(d)} volume approximation for minimum-volume β-conditioned ellipsoids with O(α/γ) coverage loss, plus a matching hardness result.
Robust estimators are hard to compute
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Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery
A poly-time algorithm achieves O(β)^{o(d)} volume approximation for minimum-volume β-conditioned ellipsoids with O(α/γ) coverage loss, plus a matching hardness result.