Before revision:  Our algorithms build on the recent sequence of works relying on certifiable anti-concentration first introduced in KKK'19, RY'20 . Our techniques expand the sum-of-squares toolkit to show robust certifiability of TV-separated Gaussian clusters in data.
After revision:  Our algorithms build on the recent sequence of works relying on certifiable anti-concentration first introduced in KKK'19, RY'20 the works of Karmarkar, Klivans, and Kothari and Raghavendra, and Yau in 2019. Our techniques expand the sum-of-squares toolkit to show robust certifiability of TV-separated Gaussian clusters in data.