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Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory.
Approximate Trace Reconstruction
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i. e., random subsequences of the string).
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