Before revision:  Our algorithm builds on the recently developed framework for list-decodable learning via the sum-of-squares (SoS)method } KKK'19, RY'20 with some key technical and conceptual advancements. Our key conceptual contribution involves showing a (SoS "certified") lower bound on the eigenvalues of covariances of arbitrary small subsamples of an i.i.d. sample of a certifiably anti-concentrated distribution. One of our key technical contributions gives a new method that allows error reduction "within SoS" with only a logarithmic cost in the exponent in the running time (in contrast to polynomial cost in KKK'19, RY'20 . In a concurrent and independent work , to have }\emph{  Raghavendra and Yau proved related results for list-decodable subspace recovery RY'20 satisfies certifiable anti-concentration, we obtain a stronger error guarantee of \|}\hat{\Pi} .
After revision:  Our algorithm builds on the recently developed framework for list-decodable learning via the sum-of-squares (SoS)method } KKK'19, RY'20  KKK'19, RY'20 . In a concurrent and independent work , to have }\emph{ Raghavendra and Yau proved related results for list-decodable subspace recovery RY'20 satisfies certifiable anti-concentration, we obtain a stronger error guarantee of \|}\hat{\Pi} .