How do noise and precision contraints jointly determine the minimum sketch size for fixed-size MinHash Jaccard estimation?
MinHash-based genome comparison is governed by two statistical constraints: a noise floor on k-mer size, controlling chance collisions between unrelated sequences, and a precision floor on sketch size, controlling uncertainty in the estimated Jaccard similarity. These constraints are best characterized for fixed-size bottom-sketch MinHash, the classical construction underlying tools such as Mash…
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