Hence, we can indeed pick in line 8 a b𝜇𝑗∈𝑀𝜇 that |𝑀𝜇∩𝐵𝑑 2𝜀′(b𝜇𝑗)|≥3 5 𝑅> 2 5 𝑅, and by Lemma A.2, there is a𝑗 ′∈[𝑘]that∥b𝜇𝑗−𝜇𝑗′∥2≤3𝜀′≤𝜀

From the proof of Lemma A

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Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms

cs.DS · 2026-01-08 · unverdicted · novelty 8.0

A poly(d,k)-time algorithm learns mixtures of k heavy-tailed spherical distributions via high-dimensional sparse Fourier transforms without needing mean separation.

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Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms cs.DS · 2026-01-08 · unverdicted · none · ref 6
A poly(d,k)-time algorithm learns mixtures of k heavy-tailed spherical distributions via high-dimensional sparse Fourier transforms without needing mean separation.

Hence, we can indeed pick in line 8 a b𝜇𝑗∈𝑀𝜇 that |𝑀𝜇∩𝐵𝑑 2𝜀′(b𝜇𝑗)|≥3 5 𝑅> 2 5 𝑅, and by Lemma A.2, there is a𝑗 ′∈[𝑘]that∥b𝜇𝑗−𝜇𝑗′∥2≤3𝜀′≤𝜀

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